
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
Let  $ ABCD$  be a trapezoid inscribed in a circle  $ \mathcal{C}$  with  $ AB\parallel CD$ ,  $ AB\equal{}2CD$ . Let  $ \{Q\}\equal{}AD\cap BC$  and let  $ P$  be the intersection of tangents to  $ \mathcal{C}$  at  $ B$  and  $ D$ . Calculate the area of the quadrilateral  $ ABPQ$  in terms of the area of the triangle  $ PDQ$ .

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