
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 a circular arc $BC$ has a radius centered at $A$ and spans an angle of $90^\circ$, and if the length of $\overarc{BC}$ is $15$, calculate the circumference of a circle that is tangent to $\overarc{BC}$, $\overarc{AC}$, and the line segment $\overline{AB}$.
A) $30 - 15\sqrt{2}$
B) $60 - 30\sqrt{2}$
C) $45 - 22.5\sqrt{2}$
D) $75 - 37.5\sqrt{2}$

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