
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
The distance between the centers of two circles is $c=714 \mathrm{~mm}$. The external common tangents intersect at an angle of $\alpha=36^{\circ} 8^{\prime}$, and the internal common tangents intersect at an angle of $\beta=104^{\circ} 12^{\prime}$. What are the radii of the circles?

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