
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]


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Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$. If the point $(n, S_n)$ (where $n$ is a positive integer) lies on the graph of the inverse function of $y = \log_2(x + 1)$, then $a_n =$ ______.

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