
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 pair of constants  $(a,b)$  such that there exists real-coefficient polynomial  $p(x)$  and  $q(x)$  that satisfies the condition below.**Condition**:  $\forall x\in \mathbb R,$   $ $   $p(x^2)q(x+1)-p(x+1)q(x^2)=x^2+ax+b$ 

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