
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 a right trapezoid \(ABCD\), the sum of the lengths of the bases \(AD\) and \(BC\) is equal to its height \(AB\). In what ratio does the angle bisector of \(\angle ABC\) divide the lateral side \(CD\)?

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