
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 a circle with center \( O \) and radius \( r \). Two parallel tangents to the circle are placed such that one tangent is at a distance \( r + 2 \) units from the center \( O \) and the other is at \( r + 4 \) units. Determine the number of points that are equidistant from the circle and these two parallel tangents.
A) 0
B) 1
C) 2
D) 3
E) 4

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