
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 quadrilateral in which  $ AB$  is parallel to  $ CD$  and perpendicular to  $ AD; AB \equal{} 3CD;$  and the area of the quadrilateral is  $ 4$ . if a circle can be drawn touching all the four sides of the quadrilateral, find its radius.

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