
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 $r$. There are three parallel tangents to this circle. Two of these tangents are equidistant from the center $O$ and are at a distance equal to the radius $r$, while the third tangent is at a distance of $r+3$ from $O$. How many points are equidistant from the circle and all three parallel tangents?

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