
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
Consider triangle  $ABC$  in  $xy$ -plane where  $ A$  is at the origin,  $ B$  lies on the positive  $x$ -axis,  $C$  is on the upper right quadrant, and  $\angle A = 30^o$ ,  $\angle B = 60^o$  , $\angle C = 90^o$ . Let the length  $BC = 1$ . Draw the angle bisector  of angle  $\angle C$ , and let this intersect the  $y$ -axis at  $D$ . What is the area of quadrilateral  $ADBC$ ?

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