
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
Given $\angle1 + \angle2 = 180^\circ$ and $\angle3 = \angle4$, find $\angle4$. In a configuration, $\angle A = 50^\circ$, $\angle B = 60^\circ$, and $\angle1$ is the angle at vertex C in triangle ABC. Another triangle DEF has $\angle D = \angle1$, $\angle E = 90^\circ$, and $\angle3$ and $\angle4$ are the angles at vertices F and E, respectively. [asy]
pair A=(0,0), B=(24,0), C=(48,0), D=(18,24), E=(12,48);
pen p=1mm+black;
draw(A--C);
draw(A--E);
draw(B--E);
draw(D--C);
label("50", A, NE);
label("60", shift(0,-7)*E, S);
label("1", B, NW);
label("2", B, NE);
label("3", shift(-4,0)*C, NW);
label("4", shift(1,-3)*D, SE);
draw(Circle((15,40), .5));
draw(Circle((5.3,3.8), .5));
[/asy]

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