
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
Two circles are externally tangent at a point. The first circle has a radius of 2 and is centered at point $C$, while the second circle has a radius of 5 and is centered at point $D$. A third circle is tangent to these two circles and the common external tangent of the first two circles. Determine the radius of this third circle.

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