
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
A suspension bridge is supported by two identical metallic cables shaped like isosceles triangles, as shown in the diagram below:

[asy]
import olympiad;
import math;

// Draw triangles
pair A = (0, 1);
pair B = (-cos(1.3089), 0);
pair C = (cos(1.3089), 0);
pair D = (2, 1);
pair E = (2-cos(1.3962), 0);
pair F = (2+cos(1.3962), 0);
draw(A--B--C--cycle);
draw(D--E--F--cycle);
draw(A--D);
label('$A$',A,N);
label('$B$',B,S);
label('$C$',C,S);
label('$D$',D,N);
label('$E$',E,S);
label('$F$',F,S);
[/asy]

If $AB = AC$ and $DE = DF$, and the angles are given by $\angle BAC = 30^\circ$ and $\angle EDF = 20^\circ$, what is the sum $\angle DAC + \angle ADE$?

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