
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  $ABC$ ,  $\angle ACB=50^{\circ}$  and  $\angle CBA=70^{\circ}$ . Let  $D$  be a foot of perpendicular from point  $A$  to side  $BC$ ,  $O$  circumcenter of  $ABC$  and  $E$  antipode of  $A$  in circumcircle  $ABC$ . Find  $\angle DAE$ 

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