
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 square with side length $a$. A new square is formed by connecting the midpoints of the sides of the first square. This process is repeated indefinitely. Calculate the limit of the sum of the perimeters of all squares thus drawn.
A) $5a$
B) $6a$
C) $7a$
D) $8a$
E) $9a$

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