
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 \(15 \times 15\) square is divided into \(1 \times 1\) small squares. From these small squares, several were chosen, and in each chosen square, one or two diagonals were drawn. It turned out that no two drawn diagonals have a common endpoint. What is the maximum number of diagonals that can be drawn? (In the solution, provide the answer, the method of drawing the diagonals, and proof that this number of diagonals is indeed the maximum possible.)

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