
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 \( x \) and \( n \) are positive integers and \( p \) is a prime number, satisfying the equation
\[ 2x^3 + x^2 + 10x + 5 = 2p^n, \]
find all possible values of \( x + n + p \).

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