
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
Triangle  $ ABC$  is isosceles with  $ AC \equal{} BC$  and  $ \angle{C} \equal{} 120^o$ . Points  $ D$  and  $ E$  are chosen on segment  $ AB$  so that  $ |AD| \equal{} |DE| \equal{} |EB|$ . Find the sizes of the angles of triangle  $ CDE$ .

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