
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 a line beginning at a length of 2 inches. This line grows following a specific sequence:
\[2 + \frac{1}{5}\sqrt{3} + \frac{1}{5} + \frac{1}{25}\sqrt{3} + \frac{1}{25} + \frac{1}{125}\sqrt{3} + \frac{1}{125} + \cdots\]
Determine the limit of this line's length if the growth process is infinite.
A) $\frac{11}{4}$
B) $\frac{10 + \sqrt{3}}{4}$
C) $\frac{12 + \sqrt{3}}{5}$
D) $\frac{13 + 2\sqrt{3}}{4}$

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