
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
Let  $ABCD$  be a parallelogram such that  $\angle BAD = 60^{\circ}.$  Let  $K$  and  $L$  be the midpoints of  $BC$  and  $CD,$  respectively. Assuming that  $ABKL$  is a cyclic quadrilateral, find  $\angle ABD.$  

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