
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 trapezoid \(ABCD\), where \(\angle BAD = 45^\circ\) and \(\angle CDA = 60^\circ\), the base \(AD\) equals 15, the base \(BC\) equals 13. A perpendicular to side \(AB\), drawn from point \(M\) (the midpoint of side \(AB\)), intersects with a perpendicular to side \(CD\), drawn from point \(N\) (the midpoint of side \(CD\)), at some point \(L\). Find the ratio of the area of triangle \(MNL\) to the area of trapezoid \(ABCD\).

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