
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
In triangle $ABC$, none of the angles is a right angle. At each vertex, the tangent line to the circumcircle of the triangle is drawn. Express the perimeter of the triangle formed by these tangents in terms of the sides of triangle $ABC$.

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