
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
The polynomial  $P$  is a quadratic with integer coefficients.  For every positive integer  $n$ , the integers  $P(n)$  and  $P(P(n))$  are relatively prime to  $n$ .  If  $P(3) = 89$ , what is the value of  $P(10)$ ?

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