
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

On the shore of a round lake, there are 6 pines growing. It is known that if you take such two triangles that the vertices of one coincide with three of the pines, and the vertices of the other coincide with the other three, then in the middle of the segment connecting the points of intersection of the heights of these triangles, there is a treasure at the bottom of the lake. It is not known, however, how to divide these six points into two groups of three. How many times will one need to dive to the bottom of the lake to surely find the treasure?

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