
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
Three sectors of a circle of radius $15$ cm overlap as shown, with centers $A$, $B$, and $C$. $A$ and $B$ form a $90^\circ$ sector, while $C$ forms a $60^\circ$ sector with the others. Determine the area of the shaded region not including any triple overlaps.

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