
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
We call the tile shown below a staircase. For which pairs \((m, n)\) of natural numbers with \(m, n \geq 6\) is it possible to cover an \(m \times n\) field with stairs without gaps or overlaps?

![](https://cdn.mathpix.com/cropped/2024_04_28_933a2e5155ae5e53e165g-6.jpg?height=140&width=143&top_left_y=424&top_left_x=1005)

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