
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 large semicircle with diameter $D$ and $N$ congruent semicircles fitting exactly on its diameter. Let $A$ be the combined area of these $N$ small semicircles, and $B$ be the area of the large semicircle that is not covered by the small semicircles. Given that the ratio $A:B$ is $1:10$, determine the value of $N$.

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