
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
There are \( 4n \) (where \( n \in \mathbb{N}^{*} \)) circles of the same radius on a plane, such that no two circles are tangent to each other, and each circle intersects with at least three other circles. Let \( f(n) \) be the number of intersection points of these circles. Find the minimum value of \( f(n) \).

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