
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
Find all values of the positive integer  $ m$  such that there exists polynomials  $ P(x),Q(x),R(x,y)$  with real coefficient satisfying the condition: For every real numbers  $ a,b$  which satisfying  $ a^m-b^2=0$ , we always have that  $ P(R(a,b))=a$  and  $ Q(R(a,b))=b$ .

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