
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 sequence of growth in the length of a line is described by the following infinite series, where the first term is the initial length of the line:
\[1 + \frac{1}{5}\sqrt{3} + \frac{1}{5} + \frac{1}{25}\sqrt{3} + \frac{1}{25} + \frac{1}{125}\sqrt{3} + \frac{1}{125} + \cdots\]
Determine the limit of the length of the line as the growth process continues indefinitely.
**A)** $\frac{27}{20}$
**B)** $\frac{1}{4}(5 + \sqrt{3})$
**C)** $\frac{1}{3}(5 + \sqrt{2})$
**D)** $\frac{7}{3}$

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