
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 sides of triangle $DEF$ are tangent to a circle with center $O$ as displayed. Given that $\angle DEF = 70^\circ$ and $\angle EFO = 40^\circ$, find $\angle DFE$, in degrees.

[asy]
unitsize(1.0 cm);

pair D, E, F, O;

D = (2.43,3.46);
E = (0,0);
F = (4.43,0);
O = incenter(D,E,F);

draw(D--E--F--cycle);
draw(incircle(D,E,F));
draw(F--O);

label("$D$", D, N);
label("$E$", E, SW);
label("$F$", F, SE);
label("$O$", O, N);

[/asy]

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