
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 polynomials  $p(x)\in\mathbb{R}[x]$  such that for all  $x\in \mathbb{R}$ : $p(5x)^2-3=p(5x^2+1)$  such that: $a) p(0)\neq 0$  $b) p(0)=0$ 

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