
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
In a $5 \times 5$ grid, each cell is painted one of five colors such that each color appears in an equal number of cells. The boundary between two adjacent cells is called a "division edge" if the colors of the two cells are different. Find the minimum number of division edges.

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