
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 rectangle $WXYZ$, $WZ = 8$ cm and $XY = 10$ cm. Point $X$ is placed on side $WY$. $XE = XF$ and the area of triangle $XEF$ is one-third the area of rectangle $WXYZ$. Determine the length in centimeters of segment $EF$ in simplest radical form.

[asy]
draw((0,0)--(0,40)--(40,40)--(40,0)--cycle);
draw((15,40)--(40,12));
label("$W$",(0,40),NW);
label("$X$",(0,0),SW);
label("$Y$",(40,0),SE);
label("$Z$",(40,40),NE);
label("$E$",(15,40),N);
label("$F$",(40,12),E);
[/asy]

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