
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 triangle  $ABC$  is given. Let  $C\ensuremath{'}$  be the vertex of an isosceles triangle  $ABC\ensuremath{'}$  with  $\angle C\ensuremath{'} = 120^{\circ}$  constructed on the other side of  $AB$  than  $C$ , and  $B\ensuremath{'}$  be the vertex of an equilateral triangle  $ACB\ensuremath{'}$  constructed on the same side of  $AC$  as  $ABC$ . Let  $K$  be the midpoint of  $BB\ensuremath{'}$  
 Find the angles of triangle  $KCC\ensuremath{'}$ .
*Proposed by A.Zaslavsky*

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