
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
Let \( m \geq n \) be positive integers. Frieder is given \( mn \) posters of Linus with different integer dimensions \( k \times l \) with \( 1 \leq k \leq m \) and \( 1 \leq l \leq n \). He must put them all up on his bedroom wall without rotating them. Every time he puts up a poster, he can either put it on an empty spot on the wall, or on a spot where it entirely covers a single visible poster and does not overlap any other visible poster. Determine the minimal area of the wall that will be covered by posters.

Answer: \( m \frac{n(n-1)}{2} \)

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