
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
Suppose there are  $n$  points in a plane no three of which are collinear with the property that if we label these points as  $A_1,A_2,\ldots,A_n$  in any way whatsoever, the broken line  $A_1A_2\ldots A_n$  does not intersect itself. Find the maximum value of  $n$ .

*Dinu Serbanescu, Romania*

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