
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
For an arithmetic sequence $b_1, b_2, b_3, \dots$, let
\[S_n = b_1 + b_2 + b_3 + \dots + b_n,\]
and let
\[T_n = S_1 + S_2 + S_3 + \dots + S_n.\]
If you are given the value of $S_{100},$ can you uniquely determine the value of $T_n$ for some integer $n$? What is this integer $n$?

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