
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  $ABCD$  is inscribed in a circle. Suppose that  $|DA| =|BC|= 2$  and $ |AB|  = 4$ . Let  $E $  be the intersection  point of lines  $BC$  and  $DA$ . Suppose that  $\angle AEB = 60^o$  and that  $|CD| <|AB|$ . Calculate the radius of the circle.

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