
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
For a positive integer \( n (n \geqslant 2) \), let \( a_n = \sum_{k=1}^{n-1} \frac{n}{(n-k) 2^{k-1}} \).
Find the maximum value in the sequence \( \{a_n\} \).

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