
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
Given an arithmetic sequence $\left\{a_n\right\}$ where all terms are distinct, satisfying $a_{2n}=2a_n-3$, and $a_6^2=a_1\cdot a_{21}$, the sum of the first $n$ terms of $\left\{a_n\right\}$ is $S_n$. Then, the maximum value among the terms of the sequence $\left\{\frac{S_n}{2^{n-1}}\right\}$ is.

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