
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
A quadratic polynomial  $p(x)$  with integer coefficients satisfies  $p(41) = 42$ . For some integers  $a, b > 41$ ,  $p(a) = 13$  and  $p(b) = 73$ . Compute the value of  $p(1)$ .

*Proposed by Aaron Lin*

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