
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 $b_1, b_2, b_3, \dots$, let $T_n$ denote the sum of the first $n$ terms of the sequence.

If $b_1 = 2$ and for all $n \geq 2$,
\[ b_n = \frac{3T_n^2}{3T_n - 2} \]
find $b_{100}$.

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