
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
The bases \(A B\) and \(C D\) of the trapezoid \(A B C D\) are 15 and 19 respectively. \( AH \) and \( BG \) are the heights to the line \(D C\), and \( CF \) is the height to the line \(A B\). Points \(K, L, M\), and \(N\) are the midpoints of the segments \(A B\), \( CF \), \( C D\), and \( A H\) respectively. Find the ratio of the area of the trapezoid \(A B C D\) to the area of the quadrilateral \(K L M N\), given that \(D G = 17\).

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