
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 $35$, two chords of length $60$ and $80$ intersect at a point whose distance from the center is $21$. The two chords divide the interior of the circle into four regions. Find the area of the region enclosed between the shorter chord, the segment connecting the chords, and the minor arc between the endpoints of the shorter chord. Express the result in the form $p\pi - q\sqrt{r}$ where $p,q,r$ are integers and $r$ is not divisible by the square of any prime. Find the sum $p+q+r$.

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