
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 circle has a diameter of $D$ divided into $2n$ equal parts. On each of these parts, a quarter-circle is constructed standing vertically from each point. Calculate the limiting value of the sum of the lengths of the arcs of these quarter-circles as $n$ becomes very large.

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