
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 square of side length $s$ is drawn. A new square is subsequently formed each time by joining the midpoints of the sides of the previous square. This process continues indefinitely. Calculate the limit of the sum of the perimeters of all the squares thus constructed.
A) $4s$
B) $6s$
C) $8s$
D) $10s$
E) $12s$

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