
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let  $P(x) = x^2 - 20x - 11$ . If  $a$  and  $b$  are natural numbers such that  $a$  is composite,  $\gcd(a, b) = 1$ , and  $P(a) = P(b)$ , compute  $ab$ .

Note:  $\gcd(m, n)$  denotes the greatest common divisor of  $m$  and  $n$ .

*Proposed by Aaron Lin*

Present the answer in LaTex format: \boxed{Your answer}
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