
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
In the diagram below, \(AB = AC = 130\), \(AD = 50\), and \(CF = 80\). Compute \(\frac{[CEF]}{[DBE]}\).

[asy]
unitsize(0.025 cm);

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

B = (0,0);
C = (100,0);
A = intersectionpoint(arc(B,130,0,180),arc(C,130,0,180));
D = interp(A,B,50/130);
F = interp(A,C,(130 + 80)/130);
E = extension(B,C,D,F);

draw(C--B--A--F--D);

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

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