
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 \(a_1, a_2, a_3, \dots,\)
\[S_n = a_1 + a_2 + a_3 + \dots + a_n,\]
and
\[T_n = S_1 + S_2 + S_3 + \dots + S_n.\]
If \(S_{2023} = 4056a + 4053d,\) for which smallest integer \(n\) can you uniquely determine \(T_n\)?

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