
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 sequence \( a_{1}, a_{2}, a_{3}, \ldots \) of positive integers satisfies \( a_{1} > 5 \) and \( a_{n+1} = 5 + 6 + \cdots + a_{n} \) for all positive integers \( n \). Determine all prime numbers \( p \) such that, regardless of the value of \( a_{1} \), this sequence must contain a multiple of \( p \).

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