
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
Let \( b_n = \frac{15^n - 1}{14} \). Define \( e_n \) as the greatest common divisor of \( b_n \) and \( b_{n+1} \). Determine the maximum possible value that \( e_n \) can take.

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