
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
Let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $S_n$, and the sum of the first $n$ terms of the sequence $\{S_n\}$ be $T_n$, satisfying $T_n=2S_n-n^2$, where $n \in \mathbb{N}^*$.

(1) Find the value of $a_1$;

(2) Find the general formula for the sequence $\{a_n\}$.

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