
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
Unit squares are arranged to form a rectangular grid that is \( m \) units wide and \( n \) units tall, where \( m \) and \( n \) are positive integers with \( 2n < m < 3n \). Determine the smallest possible value of \( mn \) such that there is a unit square in the grid that is not completely shaded but whose shaded area is greater than 0.999.

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