
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
An equilateral triangle is initially drawn with a side length of $s$. A new equilateral triangle is formed by joining the points one-third of the way along each side of the first triangle from each vertex. Another triangle is then formed by applying the same process to the second triangle, and this process is repeated indefinitely. Calculate the limit of the sum of the perimeters of all the triangles thus drawn.
A) $6s$
B) $9s$
C) $12s$
D) $15s$

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