
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 diagram, $EFGH$ is a square with side length $8,$ and $KLMN$ is a rectangle with $KL=14$ and $KM=8.$ Also, $EH$ and $KL$ are perpendicular. If the shaded area is equal to one third of the area of $KLMN,$ what is the length of $EQ?$

[asy]
draw((0,0)--(14,0)--(14,8)--(0,8)--cycle,black+linewidth(1));
draw((-2.5,2)--(5.5,2)--(5.5,10)--(-2.5,10)--cycle, black+linewidth(1));
filldraw((-2.5,2)--(5.5,2)--(5.5,8)--(-2.5,8)-- cycle,gray,black+linewidth(1));
label("$K$",(0,8),NW);
label("$L$",(14,8),NE);
label("$M$",(14,0),SE);
label("$N$",(0,0),SW);
label("$E$",(-2.5,10),NW);
label("$F$",(5.5,10),NE);
label("$G$",(5.5,2),E);
label("$H$",(-2.5,2),W);
label("$Q$",(-2.5,8),SW);
label("8",(-2.5,10)--(5.5,10),N);
label("8",(14,0)--(14,8),E);
label("14",(0,0)--(14,0),S);
[/asy]

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