
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
In the picture, there is a square grid with squares of side length \(1 \text{ cm}\). A shape shaded in gray is drawn on the grid. Libor needs to draw a line parallel to the line \(MO\) that divides the gray shape into two parts with equal area.

At what distance from the line \(MO\) should Libor draw this parallel line?

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