
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 \( p(x) = a_{n} x^{n} + a_{n-1} x^{n-1} + \ldots + a_{0} \), where each \( a_{i} \) is either 1 or -1. Let \( r \) be a root of \( p \). If \( |r| > \frac{15}{8} \), what is the minimum possible value of \( n \)?

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