
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 diagonals  $AC$  and  $BD$  of a convex quadrilateral  $ABCD$  with  $S_{ABC} = S_{ADC}$  intersect at  $E$ . The lines through  $E$  parallel to  $AD$ ,  $DC$ ,  $CB$ ,  $BA$ meet  $AB$ ,  $BC$ ,  $CD$ ,  $DA$  at  $K$ ,  $L$ ,  $M$ ,  $N$ , respectively. Compute the ratio  $\frac{S_{KLMN}}{S_{ABC}}$ 

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