
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 numbers in the sequence \( 121, 125, 131, 139, \ldots \) are of the form \( b_n = 120 + n^2 \), where \( n = 1, 2, 3, \ldots \) For each \( n \), let \( e_n \) be the greatest common divisor of \( b_n \) and \( b_{n+1} \). Find the maximum value of \( e_n \) as \( n \) ranges through the positive integers.

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