
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
Equilateral triangles  $ACB'$  and  $BDC'$  are drawn on the diagonals of a convex quadrilateral  $ABCD$  so that  $B$  and  $B'$  are on the same side of  $AC$ , and  $C$  and  $C'$  are on the same sides of  $BD$ . Find  $\angle BAD + \angle CDA$  if  $B'C' = AB+CD$ .

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