
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 with a radius of $45$, two chords, each of length $84$, intersect at a point that is $15$ units away from the center of the circle. The two chords divide the circle into four regions. Determine the area of one of the regions that is bounded by segments of unequal lengths, where the area can be expressed in the form $m\pi - n\sqrt{d}$, with $m, n,$ and $d$ as positive integers and $d$ not divisible by the square of any prime number. Find the sum $m+n+d$.

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