
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.

[asy]
unitsize(1inch);
pair D,E,F;
D = (0,0);
E = (2*sqrt(3),0);
F = (0,2);
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("$8$",F/2,W);
label("$30^\circ$",(1.25,0),N);
[/asy]

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