
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
Using $m$ colors ($m \geqslant 2$) to paint a $1 \times n$ chessboard, where each cell is painted a different color. Let $h(m, n)$ represent the number of ways to paint the chessboard so that adjacent cells have different colors and each color is used at least once. Find the formula for counting $h(m, n)$.

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