
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
For  a given positive integer  $n >2$ , let  $C_{1},C_{2},C_{3}$  be the boundaries of three convex  $n-$  gons in the plane , such that 
   $C_{1}\cap C_{2}, C_{2}\cap C_{3},C_{1}\cap C_{3}$  are finite. Find the maximum number of points of the sets  $C_{1}\cap C_{2}\cap C_{3}$ .

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