
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
If $N$ congruent semicircles rest along the diameter of a larger semicircle, completely and individually spanning the diameter without gaps, and the ratio of the total area of these small semicircles to the area of the region within the bounds of the larger semicircle but external to all the small semicircles is $1:4$, determine the calculated value of $N$.

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