
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 defined by the following progression:
\[2 + \frac{1}{3} + \frac{1}{9} + \frac{1}{3^2} + \frac{1}{9^2} + \frac{1}{3^3} + \frac{1}{9^3} + \cdots\]
Determine the limit of this series as it extends to infinity.
A) $\frac{1}{3}$
B) $3$
C) $\frac{21}{8}$
D) $2\frac{5}{8}$
E) $2.5$

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