
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 $D$ is placed on segment $AB$ such that $AD = 15$ and $DB = 10$. Point $E$ bisects angle $ACB$. Find the ratio of the area of $\triangle BCE$ to the area of $\triangle ACE$. Given the lengths of the segments are $AC = 50$ and $BC = 45$.

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