
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
Find the area of triangle $DEF$ below, which is a right isosceles triangle (45-45-90 triangle) with the hypotenuse $DE = 10$ units.

[asy]
unitsize(1inch);
pair D, E, F;
D = (0,0);
E = (1,0);
F = (0,1);
draw(D--E--F--D, linewidth(0.9));
draw(rightanglemark(E, D, F, 3));
label("$D$", D, S);
label("$E$", E, S);
label("$F$", F, N);
label("$10$", (0.5,0.5), NE);
[/asy]

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