
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
Consider two concentric circles centered at the origin, one with a radius of $1$ and another with a radius of $2$. Let $A$ and $B$ be the endpoints of a diameter of the smaller circle. Find the number of points $P$ inside the larger circle, such that the sum of the squares of distances from $P$ to $A$ and $B$ is $5$.
A) 0
B) 1
C) 2
D) 4
E) Infinite

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