
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
Consider a modified "$n$-pointed star" formed in the following way: sides of a convex polygon are numbered consecutively as $1,2, …, k, …, n$ $(n \geq 6)$. For all values of $k$, sides $k$ and $k+3$ (consider modulo $n$ such that side $n+1$ is side $1$ and so forth) are non-parallel. Extend these $n$ pairs of sides numbered $k$ and $k+3$ until they meet. Given this setup, let $T$ represent the degree-sum of the interior angles at the $n$ points of this modified star. Express $T$ as a function of $n$.
A) \( 180 (n-1) \)
B) \( 180 (n-2) \)
C) \( 180 (n-3) \)
D) \( 180 (n-4) \)

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