
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
Let $p(x) = x^2 + bx + c,$ where $b$ and $c$ are integers. If $p(x)$ is a factor of both $x^4 + 8x^2 + 49$ and $2x^4 + 5x^2 + 35x + 7$, what is $p(1)$?

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