
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
Let  $\gamma_1, \gamma_2,\gamma_3 $  be three circles of unit radius which touch each other externally.  The common tangent to each pair of circles are drawn (and extended so that they intersect) and let the triangle formed by the common tangents be  $\triangle XYZ$  . Find the length of each side of  $\triangle XYZ$ 

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