
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
A quadrilateral \(ABCD\) has an area of 1. From an internal point \(O\), perpendiculars \(OK\), \(OL\), \(OM\), and \(ON\) are dropped to the sides \(AB\), \(BC\), \(CD\), and \(DA\) respectively. It is known that \(AK \geq KB\), \(BL \geq LC\), \(CM \geq MD\), and \(DN \geq NA\). Find the area of quadrilateral \(KLMN\).

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