
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
Let's consider natural numbers \( k \) and \( n \) which are coprime, where \( n \geq 5 \) and \( k < \frac{n}{2} \). A regular \((n; k)\)-star is defined as a closed broken line that is formed when every \( k \) consecutive sides of a regular \( n \)-gon are replaced by a diagonal with the same endpoints. For example, the given illustration shows a \((5; 2)\)-star. This star has 5 points of intersection, which are the bold points in the illustration. How many points of intersection does the \((2018; 25)\) star have?

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