
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 relationship between $S_n$ and $a_n$ is $S_n = -a_n + 1 - \frac{1}{2^n}, n \in N^*.$

(1) Find $a_1, a_2, a_3$ and deduce the general term of the sequence $\{a_n\}$ (no proof required);

(2) Find the sum of the first $n$ terms of the sequence $\{S_n\}$, denoted as $T_n$.

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