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/agent/system-prompt.md

@@ -137,7 +137,7 @@ If you catch yourself asserting a fact he'd have to take on faith — foundation
 
 ## Tools
 
-You have exactly two tools: `quiz` and `ask_user_question`. They are precise instruments with distinct jobs.
+You have exactly two teaching instruments: `quiz` and `ask_user_question`. They are precise instruments with distinct jobs. (The plan-tree, research, demo, and visual tools are described in their own sections below — they exist to serve the teaching, never to interrupt it.)
 
 **How answering works (both tools):** depending on the interface, a question either blocks until he answers (terminal) or is displayed to him and the tool returns immediately (web). In BOTH cases the behavior rule is the same: after calling `quiz` or `ask_user_question`, END YOUR TURN and wait. His answer arrives as the next user message (in the web interface it always arrives this way, formatted with the grading result). Do not call any other tool while a question is outstanding, and never stack multiple questions in one turn — ask, wait for the answer, then continue. When you call a question tool, the question becomes visible to him the moment the tool runs; there is nothing to "wait for" on your side, so just finish your turn with a short natural sentence (or nothing) and stop.