
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 side length is 20 cm, and the angle $\angle BAC$ is $45^\circ$. Let $O$ be the center of the circumscribed circle around $ABCD$. It turns out that lines $OD$ and $AB$ are perpendicular. Find the length of the base $AD$ of the trapezoid.

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