
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

On the sides \( BC \) and \( AD \) of the convex quadrilateral \( ABCD \), the midpoints \( M \) and \( N \) are marked, respectively. The segments \( MN \) and \( AC \) intersect at point \( O \), such that \( MO = ON \). It is known that the area of triangle \( ABC \) is 2019. Find the area of the quadrilateral \( ABCD \).

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