
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 a sheet of paper, 25 points are marked as the centers of the cells of a $5 \times 5$ square grid. The points are colored in several colors. It is known that no three points of the same color lie on a single straight line (whether vertical, horizontal, or diagonal). What is the minimum number of colors that could have been used? (20 points)

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