
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 \( a_1, a_2, a_3, \dots \), let \( S_n \) denote the sum of the first \( n \) terms of the sequence.

If \( a_1 = 1 \) and
\[ a_n = \frac{3S_n^2}{3S_n - 2} \text{ for all } n \geq 2, \]
then find \( a_{100} \).

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