
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, $PQ = PR = 130,$ $PS = 45,$ and $RT = 90.$  Compute $\frac{[RTF]}{[SBE]}.$

[asy]
unitsize(0.025 cm);

pair P, Q, R, S, T, F, E;

Q = (0,0);
R = (100,0);
P = intersectionpoint(arc(Q,130,0,180),arc(R,130,0,180));
S = interp(P,Q,45/130);
T = interp(P,R,(130 + 90)/130);
E = extension(Q,R,S,T);

draw(R--Q--P--T--S);

label("$P$", P, N);
label("$Q$", Q, SW);
label("$R$", R, NE);
label("$S$", S, W);
label("$T$", T, SE);
label("$E$", E, SW);
label("$F$", F, SE);
[/asy]

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