
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
A regular pentagon is inscribed in a circle. There is a circle that passes through each exterior angle vertex of the pentagon formed by extending the sides of the pentagon. Calculate the sum of the measures of the angles between the external tangent lines at these points where they touch the second circle.

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