
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
The sequence \( p_{n} \) is defined recursively. Let \( p_{1} = 2 \) and \( p_{n+1} \) be the largest prime factor of \( p_{1} p_{2} \ldots p_{n} + 1 \). Does the number 11 appear in the sequence?

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