
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
Calculate the ratio of the area of $\triangle BCX$ to the area of $\triangle ACX$ in the diagram if line $CX$ bisects $\angle ACB$. See the diagram below:
- $BC = 36$ units
- $AC = 45$ units
- The line $CX$ is the angle bisector of $\angle ACB$.
Express your answer as a common fraction.

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