
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
Points $A$, $B$, $C$, $D$, and $E$ lie on the circle shown, and the measures of arcs $AB$ and $DE$ are $60^\circ$ and $72^\circ$, respectively. Given that point $F$ is the intersection of chords $AC$ and $BD$, find the sum of the measures of angles $F$ and $C$, in degrees.

[asy]
import graph;

unitsize(2 cm);

pair A, B, C, D, E, F;

A = dir(110);
B = dir(50);
C = dir(170);
D = dir(-10);
E = dir(-70);
F = extension(A,C,B,D);

draw(Circle((0,0),1));
draw(A--C);
draw(B--D);
draw(A--B);
draw(D--E);

label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, SW);
label("$D$", D, SE);
label("$E$", E, S);
label("$F$", F, N);
[/asy]

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