
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 circle  $\omega$  has center  $O$  and radius  $r$ . A chord  $BC$  of  $\omega$  also has length  $r$ , and the tangents to  $\omega$  at  $B$  and  $C$  meet at  $A$ . Ray  $AO$  meets  $\omega$  at  $D$  past  $O$ , and ray  $OA$  meets the circle centered at  $A$  with radius  $AB$  at  $E$  past  $A$ . Compute the degree measure of  $\angle DBE$ .

*Author: Ray Li*

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