
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 area of polygon $ABCDEF$ is 75. The lengths of sides are given as $AB=7$, $BC=10$, and $FA=6$. Assume $\overline{DE}$ is parallel to $\overline{AB}$, and the horizontal distance from $D$ to $F$ is 8. Calculate $DE+EF$. [asy]
pair a=(0,8), b=(7,8), c=(7,0), d=(5,0), e=(5,3), f=(0,3);
draw(a--b--c--d--e--f--cycle);
draw(shift(0,-.25)*a--shift(.25,-.25)*a--shift(.25,0)*a);
draw(shift(-.25,0)*b--shift(-.25,-.25)*b--shift(0,-.25)*b);
draw(shift(-.25,0)*c--shift(-.25,.25)*c--shift(0,.25)*c);
draw(shift(.25,0)*d--shift(.25,.25)*d--shift(0,.25)*d);
draw(shift(.25,0)*f--shift(.25,.25)*f--shift(0,.25)*f);
label("$A$", a, NW);
label("$B$", b, NE);
label("$C$", c, SE);
label("$D$", d, S);
label("$E$", e, SW);
label("$F$", f, SW);
label("6", (0,5.5), W);
label("7", (3.5,8), N);
label("10", (7, 1.5), E);
[/asy]

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