
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
A paper square was punctured at 1965 points. No three of the puncture points or the vertices of the square lie on the same line. Then, several straight, non-intersecting cuts were made, each starting and ending only at the puncture points or the vertices of the square. It turned out that the square was cut into triangles, none of which contains any puncture points inside. How many cuts were made and how many triangles were obtained?

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