
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 trapezoid \(ABCD\), \(AB = 4\), \(CD = 6\), \(\angle DAB = 90^\circ\), \(\angle BCD = 45^\circ\), and \(AB\) is parallel to \(CD\). What is the length of \(BD\)? 

![Trapezoid ABCD](https://cdn.mathpix.com/cropped/2024_04_17_587bc2a8915214d42f9eg-2.jpg?height=233&width=680&top_left_y=290&top_left_x=777)

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