
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 $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$. Given that $S_n = (-1)^n a_n - \frac{1}{2^n}$ for $n \in \mathbb{N}^*$, find  
(1) $a_3 = \_\_\_\_\_\_$;  
(2) $S_1 + S_2 + \ldots + S_{100} = \_\_\_\_\_\_$.

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