
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
Given that a star polygon is created by extending sides of an n-sided convex polygon where, for each side k (with sides numbered from 1 to n), side k is extended to intersect with side k+3, considering indices modulo n (where side n+k corresponds to side k), calculate the total sum of the internal angles at the intersections forming the vertices of this newly defined n-pointed star.

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