
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 diagram below shows a circle with center  $F$ . The angles are related with  $\angle BFC = 2\angle AFB$ ,  $\angle CFD = 3\angle AFB$ ,  $\angle DFE = 4\angle AFB$ , and  $\angle EFA = 5\angle AFB$ . Find the degree measure of  $\angle BFC$ .
[asy]
size(4cm);
pen dps = fontsize(10);
defaultpen(dps);
dotfactor=4;
draw(unitcircle);
pair A,B,C,D,E,F;
A=dir(90);
B=dir(66);
C=dir(18);
D=dir(282);
E=dir(210);
F=origin;
dot(" $F$ ",F,NW);
dot(" $A$ ",A,dir(90));
dot(" $B$ ",B,dir(66));
dot(" $C$ ",C,dir(18));
dot(" $D$ ",D,dir(306));
dot(" $E$ ",E,dir(210));
draw(F--E^^F--D^^F--C^^F--B^^F--A);
[/asy]

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