
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
In a circle of radius $15$, a sector has a central angle of $90^\circ$. Inside the sector, a triangle is drawn with vertices at the center and two other points on the arc, where these points divide the arc into three equal segments. Calculate the area of the triangle.

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