
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 the polynomial $p(x),$ with real coefficients, such that $p(2) = 8$ and
\[p(x) p(y) = p(x) + p(y) + p(xy) - 2\]for all real numbers $x$ and $y.$

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