
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 $5 \times 5$ grid consists of 25 $1 \times 1$ small squares. Each small square is divided into four identical isosceles triangles, three of which are colored black. If a side of a small square is on a black part, it is called a black edge; otherwise, it is a white edge. In the $5 \times 5$ grid, the common edge of adjacent (sharing a common edge) small squares must be the same color. What is the minimum number of black edges on the four sides of the $5 \times 5$ grid?

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