
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 told the value of $S'_{3028}$, then you can 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}
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