
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
In  $\triangle ABC$  points  $M,O$  are midpoint of  $AB$  and circumcenter. It is true, that  $OM=R-r$ . Bisector of external  $\angle A$  intersect  $BC$  at  $D$  and bisector of external  $\angle C$  intersect  $AB$  at  $E$ . 
Find possible values of  $\angle CED$ *D. Shiryaev*

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