
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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