
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 a sequence $\{a_n\}$ whose sum of the first n terms is $S_n = 2^n + c$ (where $n \in \mathbb{N}^*$, and c is a constant),
(1) If the sequence $\{a_n\}$ is a geometric progression, find the value of the constant c;
(2) If $c = 2$, find the general formula for the terms in the sequence $\{a_n\}$.

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