Match the pi learning system's tool definitions (quiz/ask)

Compared the port against the original pi setup
(vault/π/learn/.pi: quiz.ts, ask-user-question.ts, teach SKILL.md) —
the pi version never produced invalid correctAnswer values. Root cause
of the port's validation failures: the pi options schema's 'Give each
option a stable value; you reference the correct one by that value in
correctAnswer' sentence was dropped in the port. Without it the model
omits values and must copy a long natural-language label verbatim into
correctAnswer — and instead slugifies it ('cultural-diagnosis' for
'A cultural diagnosis') every turn.

Now matched to pi:
- quiz schema: pi's field order (question, details, options,
  multiSelect, correctAnswer, explanation) and descriptions — options
  carry the stable-value instruction, correctAnswer is phrased as a
  value reference ('the value field of the option you intend'), not a
  copy-exact-or-fail threat. nodeId (lh-only, graph) stays.
- ask schema: dropped the redundant 'mode' param (pi has none; the dock
  already infers from options presence), pi's descriptions.
- quiz tool description: pi's full text (ask contrast, note field,
  dontKnow semantics) minus terminal-only details, plus lh's turn
  protocol sentence.
- system-prompt: fixed the stale 'exactly two tools' line (plan/research/
  demo/visual tools have their own sections).

Not matched, deliberately: tool results stay JSON (pi sends curated
text; formatAnswerMessage exists if we want it later), shuffle param
(lh always shuffles seeded), pi's ask '(Recommended)' label hint.

src/core/question-core.ts

@@ -109,25 +109,35 @@ export function quizInputProblems(input: {
 
 export const quizInputSchema = z
 	.object({
-		question: z.string().describe("The single quiz question to ask"),
+		question: z.string().describe("The single quiz question to ask. Ask exactly one question per tool call."),
 		options: z
 			.array(optionSchema)
 			.min(2)
 			.describe(
-				"The answer options (2 or more). Options only — no free-text mode. Never add your own 'I don't know' option.",
+				"The answer options (2 or more). Options only — there is no free-text mode. " +
+					"Give each option a stable `value`; you reference the correct one by that value in correctAnswer. " +
+					"Never add your own 'I don't know' option — that choice is added for you.",
 			),
+		multiSelect: z
+			.boolean()
+			.optional()
+			.describe("Set to true when more than one option is correct and the learner must select all of them."),
 		correctAnswer: z
 			.union([z.string(), z.array(z.string())])
 			.describe(
-				"The correct answer as the option value(s): copy the EXACT `value` — or `label` when `value` is omitted — " +
-					"of the intended option(s), never a paraphrase or slug; a mismatch fails validation. " +
-					"Single-select: one string. Multi-select: an array; the learner is only correct if their selection matches this set exactly.",
+				"REQUIRED. The correct answer as the option value(s) — the `value` field of the option you intend. " +
+					'Single-select: a single string (e.g. "mercury"). Multi-select: an array of strings (e.g. ["belize", "niue"]); ' +
+					"the learner is only correct if their selection matches this set exactly. " +
+					"Always pass the value, not a position number — this is self-checking and prevents miscounting. " +
+					"A value that matches no option fails validation and the call is returned to you to fix.",
 			),
 		explanation: z
 			.string()
-			.describe("Explanation revealed AFTER the learner answers. Always say why the correct answer is correct."),
-		multiSelect: z.boolean().optional().describe("Set true only when more than one option is correct"),
-		details: z.string().optional().describe("Optional extra context or instructions shown under the question"),
+			.describe(
+				"REQUIRED. Explanation revealed AFTER the learner answers (shown whether they got it right or wrong). " +
+					"Use it to reinforce why the correct answer is correct.",
+			),
+		details: z.string().optional().describe("Optional extra context or instructions shown under the question."),
 		nodeId: z
 			.string()
 			.optional()
@@ -150,22 +160,20 @@ export const quizInputSchema = z
 
 export const askInputSchema = z
 	.object({
-		question: z.string().describe("The single question to ask"),
-		mode: z
-			.enum(["single-select", "multi-select", "text"])
-			.optional()
-			.describe(
-				"Answer mode. Omit for single-select when options are given, or text when they are not.",
-			),
+		// No `mode` param — the pi original has none: the mode is inferred from
+		// whether options are present (the dock does exactly this). One less
+		// knob for the model to misuse.
+		question: z.string().describe("The single question to ask the learner. Ask exactly one question per tool call."),
+		details: z.string().optional().describe("Optional extra context or instructions shown under the question."),
 		options: z
 			.array(optionSchema)
 			.min(2)
 			.optional()
 			.describe(
-				"Optional multiple-choice options. Omit for free-form text input. The learner can always choose 'Other' and type a custom answer.",
+				"Optional multiple-choice options. Omit for free-form text input. " +
+					"The learner can always choose 'Other' and type a custom answer when options are provided.",
 			),
-		multiSelect: z.boolean().optional().describe("Set true to allow multiple answers to be selected"),
-		details: z.string().optional().describe("Optional extra context or instructions shown under the question"),
+		multiSelect: z.boolean().optional().describe("Set to true to allow multiple answers to the same question."),
 	})
 	// Same option sanity as the quiz (labels non-empty, values distinct — ask
 	// is not graded, but duplicate values break the dock's value keying).