
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 given diagram, $CY$ bisects $\angle BCA$ and $CX$ bisects $\angle ACB$. Let $AB = 35$, $BC = 40$, and $AC = 45$. Find the ratio of the area of $\triangle BCY$ to the area of $\triangle ACX$. Assume point $X$ is on line segment $AB$ and point $Y$ is on line segment $AC$. Express your answer as a common fraction. [asy]
import markers;

real s=40/(40+45);
real t=45/(45+35);
pair A=(-15.57,0);
pair B=(8.43,0);
pair C=(0,25.65);
pair X=t*A+(1-t)*B;
pair Y=s*B+(1-s)*C;

draw(C--A--B--C--X--C--Y);

label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,N);
label("$X$",X,NE);
label("$Y$",Y,NW);

label("$35$",.5*(B+A),S);
label("$40$",.5*(B+C),E);
label("$45$",.5*(A+C),W);
[/asy]

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