
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
The bisector of angle $B A D$ of the right trapezoid $A B C D$ (with bases $A D$ and $B C$, and $\angle B A D=90^{\circ}$) intersects the lateral side $C D$ at point $E$. Find the ratio $C E: E D$ if $A D+B C=A B$.

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