
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 \( a_1, \) \( a_2, \) \( a_3, \) \(\dots,\) let
\[ S_n = a_1 + a_2 + a_3 + \dots + a_n, \]and let
\[ T_n = S_1 + S_2 + S_3 + \dots + S_n. \]If you know the value of \( S_{2023}, \) 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}
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