
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 $b_n = \frac{10^n - 2}{8}$. Define $e_n$ to be the greatest common divisor of $b_n$ and $b_{n+2}$. Find the maximum possible value that $e_n$ can take on.

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