
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
Two sectors are cut from two different circles, with one having a radius of 15, and the other having a radius of 10. The first sector has a central angle of 90 degrees, and the second sector has a central angle of 120 degrees. Place these sectors side by side such that they are symmetric about a vertical line passing through their common vertex. Find the total area of this composition.

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