
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
Let $p \geq 3$ be a prime number. Each side of a triangle is divided into $p$ equal parts, and each of the division points is connected to the opposite vertex. Calculate the maximum number of pairwise disjoint regions into which the triangle is divided.

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