
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
Determine all 2nd degree polynomials with integer coefficients of the form  $P(X)=aX^{2}+bX+c$ , that satisfy:  $P(a)=b$ ,  $P(b)=a$ , with  $a\neq b$ .

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