
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 modified infinite series $1 - \frac{1}{3} - \frac{1}{9} + \frac{1}{27} - \frac{1}{81} - \frac{1}{243} + \frac{1}{729} - \cdots$. Find the sum $T$ of this series.
A) $\frac{1}{156}$
B) $\frac{5}{78}$
C) $\frac{1}{39}$
D) $\frac{1}{12}$
E) $\frac{1}{3}$

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