
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 convex quadrilateral \(ABCD\), point \(L\) is the midpoint of side \(BC\), point \(M\) is the midpoint of side \(AD\), and point \(N\) is the midpoint of side \(AB\). Find the ratio of the area of triangle \(LMN\) to the area of quadrilateral \(ABCD\).

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