
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
Consider the function  $f(x)=5x^4-12x^3+30x^2-12x+5$ . Let  $f(x_1)=p$ , wher  $x_1$  and  $p$  are non-negative integers, and  $p$  is prime. Find with proof the largest possible value of  $p$ .
*Proposed by tkhalid*

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