
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 $ABCDEFGH$ is 85 with $AB=7$, $BC=10$, and $HA=6$. What is the sum $DE + EF + FG + GH$? Below is the diagram and dimensions:
[asy]
pair a=(0,10), b=(7,10), c=(7,0), d=(3,0), e=(3,3), f=(0,3), g =(-3,3), h =(-3,10);
draw(a--b--c--d--e--f--g--h--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)*h--shift(.25,.25)*h--shift(0,.25)*h);
label("$A$", a, NW);
label("$B$", b, NE);
label("$C$", c, SE);
label("$D$", d, S);
label("$E$", e, SW);
label("$F$", f, W);
label("$G$", g, SW);
label("$H$", h, NW);
label("6", (0,8.5), W);
label("7", (3.5,10), N);
label("10", (7, 5), E);
[/asy]

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