
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 is an equilateral triangle  $ABC$  on the plane. Three straight lines pass through  $A$ ,  $B$  and  $C$ , respectively, such that the intersections of these lines form an equilateral triangle inside  $ABC$ . On each turn, Ming chooses a two-line intersection inside  $ABC$ , and draws the straight line determined by the intersection and one of  $A$ ,  $B$  and  $C$  of his choice. Find the maximum possible number of three-line intersections within  $ABC$  after 300 turns.
*Proposed by usjl*

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