
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 parallel tangents. One tangent is at a distance of $r$ from the center, and the other is at a distance of $r+2$ from the center. Determine the number of points that are equidistant from the circle and these two tangents.

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