
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
Let $n$ be the number of points $P$ interior to the region bounded by a circle with radius $2$, such that the sum of squares of the distances from $P$ to the endpoints of a given diameter is $10$ and the angle $\angle APB = 60^\circ$. Then, $n$ is:
A) 0
B) 1
C) 2
D) 4
E) Infinite

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