
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 triangle $ABC$, point $X$ is on line segment $AB$ and point $Y$ is on line segment $AC$ such that $BX$ bisects $\angle ABC$ and $CY$ bisects $\angle ACB$. Given that $AB = 35$, $AC = 42$, and $BC = 48$, find the ratio of the area of $\triangle BCY$ to the area of $\triangle BAX$. Express your answer as a simplified fraction.

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