
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 $S_n$ be the sum of the first $n$ terms of a positive sequence $\{ a_n \}$, given $a_1 = 2$ and $S_{n+1}(S_{n+1} - 2S_n + 1) = 3S_n(S_n + 1)$, find the value of $a_{100}$.

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