
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 $\{a\_n\}$, the sum of its first $n$ terms, $S\_n$, satisfies $S\_n = 3a\_n - 2$. The sum of the first $n$ terms of the sequence $\{na\_n\}$ is $T\_n$. Find the smallest value of $n$ such that $T\_n > 100$.

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