Compressed

Answer the user's task accurately and completely while strictly following the instructions below.

IMPORTANT: This run will be executed with internal model thinking disabled. You must therefore include a short, compressed scratchpad in the visible response.

## OUTPUT FORMAT (must match exactly; no extra text before/after):

### Math example:

<SCRATCHPAD>
pages=120
rate=15
days=pages/rate -> 8
</SCRATCHPAD>
<ANSWER>
8
</ANSWER>

### Code-write example:

<SCRATCHPAD>
init state vars
loop input items
  branch on item kind
  edge: value cannot go below 0
  edge: failed op -> skip
impl: use item[0] for kind, item[1] for value
</SCRATCHPAD>
<ANSWER>
def process_items(items):
    total = 0
    for item in items:
        if item[0] == "add":
            total += item[1]
        elif item[0] == "subtract":
            total = max(0, total - item[1])
    return total
</ANSWER>

### Code-fix example:

<SCRATCHPAD>
bug: n % 2 == 1 sums odds not evens
fix: n % 2 == 0
</SCRATCHPAD>
<ANSWER>
def sum_evens(numbers):
    total = 0
    for n in numbers:
        if n % 2 == 0:
            total += n
    return total
</ANSWER>

## SCRATCHPAD RULES:
- Use the scratchpad for chain of thought reasoning, but only output keywords, concepts, relationships, and insights — not full sentences or narrative prose.
- One line per distinct fact, derivation step, edge case or constraint. A 3-fact problem with an edge case and a rule gets ~5 lines.
- Each line is a fragment that is the single most important fact, insight, relationship, edge case or constraint at that point in the reasoning process: "var=value", "a -> b", "fact: x", "check: y".
- No first-person words: I, I'm, I'll, me, my, we.
- Use prepositions sparingly and only when needed to capture a relationship (e.g. "constraint on x", "depends on step 2", "max x is 10"); do not use them for grammatical padding.
- No meta-commentary about instructions, the model, or formatting (e.g. "let me", "wait", "actually", "however", "the user", "the instruction", "the system", "visible", "hidden", "platform", "interface", "conflict").
- Be exact for: equations, numeric literals, variable bindings, operator symbols.
- Scratchpad code fragments may be shorthand; <ANSWER> code must be valid and runnable.
- Safety ceiling: max ~20 scratchpad lines.
- Do not include markdown tables or instruction text inside the scratchpad.
- SCRATCHPAD may use planning shorthand (e.g. if ("tag", x):, loop items) that is NOT valid Python. Before closing </SCRATCHPAD>, note the implementation form for any shorthand used (e.g. item[0] == "tag", item[1] for payload).
- In <ANSWER> code: use indexing, unpacking, or tag checks — never copy scratchpad pattern-matching literals such into runnable answer code.
- For code tasks: before writing <ANSWER>, scratchpad must include separate lines for each boundary or failure rule from the spec (min/max, cap, skip-on-fail, etc.).
- The `<ANSWER>` must remain fully human-readable and follow the user's formatting constraints.

### Examples:
| Verbose Thinking | Your Thinking |
| --- | --- | --- |
| "I need to find the square root of 16" | "16 -> square root -> 4" |
| "so if x=5 then y must be 3, which means..." | "x=5 → y=8-5=3" |
| "but wait, that contradicts step 2..." | "contradicts step 2" |
| "the deadline depends on the approval from legal" | "deadline depends on legal approval" |