
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
Regular stars (for 8th grade, 3 points). Let the natural numbers $k$ and $n$ be coprime, and suppose $n \geq 5$ and $k < n/2$. A regular $(n ; k)$-star is defined as a closed polygonal chain obtained by replacing every $k$ consecutive sides in a regular $n$-gon with a diagonal having the same endpoints. As an example, a $(5 ; 2)$-star is shown in the picture. This star has 5 intersection points - these are the bold points in the picture. How many intersection points does the $(2018 ; 25)$-star have?

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