
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 an infinite chessboard, two squares are said to touch if they share at least one vertex and they are not the same square. Suppose that the squares are colored black and white such that

- there is at least one square of each color;
- each black square touches exactly \( m \) black squares;
- each white square touches exactly \( n \) white squares

where \( m \) and \( n \) are integers. Must \( m \) and \( n \) be equal?

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