
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
Given a large semicircle with radius R and N congruent smaller semicircles inside, each lying on the diameter of the large semicircle and having their diameters completely covering this diameter without gaps or overlaps, find the value of N if the ratio of the total area of the smaller semicircles to the area of the region inside the large semicircle but outside all the smaller semicircles is 1:36.

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