
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
In a plane, there are $n$ ($n \in \mathbb{N}^*$) circles such that every two circles intersect, but no three circles intersect at a single point. If these $n$ circles divide the plane into $f(n)$ regions, then find the expression for $f(n)$.

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