
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
Consider the infinite series $1 + \frac{1}{2} - \frac{1}{4} - \frac{1}{8} + \frac{1}{16} + \frac{1}{32} - \frac{1}{64} - \frac{1}{128} + \cdots$. Let $S$ be the (limiting) sum of this series.
**A)** $\frac{1}{5}$
**B)** $\frac{4}{5}$
**C)** $\frac{6}{5}$
**D)** $\frac{8}{5}$
**E)** $\frac{9}{5}$

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