
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
Given the sequence \{a_n\}, it satisfies S_n = 1 - a_n (n \in \mathbb{N}^*), where S_n is the sum of the first n terms of \{a_n\}.
(1) Find the general formula for \{a_n\};
(2) If the sequence \{b_n\} satisfies b_n = 2^n * a_n (n \in \mathbb{N}^*), find the formula for the sum of the first n terms of \{b_n\}, denoted as T_n.

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