
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 $1 + \frac{1}{2} - \frac{1}{4} + \frac{1}{8} + \frac{1}{16} - \frac{1}{32} + \frac{1}{64} + \frac{1}{128} - \frac{1}{256} + \cdots$. Let $T$ be the (limiting) sum of this series. Find the value of $T$.
A) $\frac{8}{7}$
B) $\frac{9}{7}$
C) $\frac{10}{7}$
D) $\frac{11}{7}$
E) $\frac{12}{7}$

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