
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 $ABCDEFG$ is 120 with $AB = 10$, $BC = 15$, and $GA = 7$. What is $DE + EF$?
[asy]
pair a=(0,12), b=(10,12), c=(10,0), d=(6,0), e=(6,5), f=(0,5), g=(-3,7);
draw(a--b--c--d--e--f--g--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, W);
label("$F$", f, W);
label("$G$", g, SW);
label("10", (5,12), N);
label("15", (10, 6), E);
label("7", (-1.5,9.5), SW);
[/asy]

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