
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
For the infinite series $1-\frac13-\frac19+\frac{1}{27}-\frac{1}{81}-\frac{1}{243}+\frac{1}{729}-\frac{1}{2187}-\cdots$, let $S$ be the (limiting) sum. Determine the value of $S$.
**A)** $\frac{15}{26}$
**B)** $\frac{27}{52}$
**C)** $\frac{45}{88}$
**D)** $\frac{60}{117}$
**E)** $\frac{30}{57}$

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