
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
A line initially 2 inches long grows according to the following law, where the first term is the initial length.
\[ 2 + \frac{1}{3}\sqrt{3} + \frac{1}{3} + \frac{1}{9}\sqrt{3} + \frac{1}{9} + \frac{1}{27}\sqrt{3} + \frac{1}{27} + \cdots \]
If this growth process continues indefinitely, find the limit of the length of the line.
- A) 3
- B) $3\sqrt{3}$
- C) $\frac{1}{2}(6 + \sqrt{3})$
- D) $6$
- E) $6\sqrt{3}$

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