
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
Given two circles, we want to draw a common tangent - a line that touches both circles. How many such lines exist? (The answer depends on the ratio of the circles' radii and the distance between their centers.)

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