
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 \( m \) 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 \( 5 \) and \( P \) lies on a straight line passing through the center of the circle. Determine \( m \).
A) 0
B) 1
C) 2
D) 3
E) Infinite

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