
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 a sequence $a_1, a_2, a_3, \dots,$ define $S_n$ as the sum of the first $n$ terms of the sequence, where $a_1 = 1$ and for all $n \ge 2$,
\[ a_n = \frac{3S_n^2}{3S_n - 2}. \]
Find $a_{100}$.

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