
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 radius $48$, two chords, each of length $90$, intersect at a point whose distance from the center is $24$. The intersecting point creates four regions inside the circle. Calculate the areas of each of these regions if two are adjacent regions bordered by segments of unequal lengths and express them in the form $p\pi - q\sqrt{r}$, where $p, q, r$ are positive integers, and $r$ is not divisible by the square of any prime number. Find $p+q+r$.

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