
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
A cubic polynomial \(p(x)\) satisfies
\[ p(n) = \frac{1}{n^2} \] for \(n = 1, 2, 3, 4, 6\). If \(p(0) = -\frac{1}{25}\), find \(p(5)\).

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