
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 an infinite series defined as:
\[ 2 + \frac{1}{2}\sqrt{3} + \frac{1}{2} + \frac{1}{8}\sqrt{3} + \frac{1}{8} + \frac{1}{32}\sqrt{3} + \frac{1}{32} + \cdots \]
Determine the limit of this series as it progresses indefinitely.
A) $\frac{2}{3}(4 + \sqrt{2})$
B) $\frac{4}{3}$
C) $\frac{8}{3}$
D) $\frac{1}{3}(4 + \sqrt{3})$
E) $\frac{2}{3}(4 + \sqrt{3})$

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