
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 an isosceles trapezoid \(ABCD\) with bases \(AD\) and \(BC\) (\(AD > BC\)), the lateral side is 40 cm, and the angle \(\angle BAC\) is \(45^\circ\). Let \(O\) be the center of the circle circumscribed around \(ABCD\). It turns out that point \(O\) lies on the line connecting point \(D\) to the midpoint of side \(AB\). Find the length of the base \(AD\) of the trapezoid.

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