
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 son of the mathematics professor. The mathematics professor wrote on the board a polynomial \( f(x) \) with integer coefficients and said:

- Today is my son's birthday. If his age \( A \) is substituted into this polynomial in place of \( x \), the result is \( f(A) = A \). Notice also that \( f(0) = P \), where \( P \) is a prime number greater than \( A \).

How old is the professor's son?

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