
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
A quadrilateral \( A B C D \) has the following properties:

- Sides \( A B \) and \( C D \) are parallel,
- There is a right angle at vertex \( B \),
- Triangle \( A D B \) is isosceles with base \( A B \),
- Sides \( B C \) and \( C D \) are each \( 10 \text{ cm} \) long.

Determine the area of this quadrilateral.

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