
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
Given that \( p \) is a prime number, \( n \) is a positive integer, and non-negative integers \( a_0, a_1, \cdots, a_n \) are all less than \( p \), satisfying the conditions
\[ 
\begin{cases}
a_1 + a_2 + \cdots + a_n = 13, \\
a_0 + a_1 p + \cdots + a_n p^n = 2015.
\end{cases}
\]
find the prime number \( p \).

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