
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 the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted as $S_n$. It is known that $\frac{1}{S_1} + \frac{1}{S_2} + \ldots + \frac{1}{S_n} = \frac{n}{n+1} \left(n \in \mathbb{N}^*\right)$. Find $a_n$.

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