
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
A circle with center \( O \) and radius \( r \) has two tangents; one is a horizontal line at a distance \( d > r \) above the circle, and the second tangent intersects the first at a point \( P \) at distance \( d \) from \( O \). Find the number of points equidistant from the circle and the two tangents.
A) 0  
B) 2  
C) 3  
D) 4  
E) ∞

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