
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
Convex quadrilateral  $ABCD$  satisfies  $\angle{CAB} = \angle{ADB} = 30^{\circ}, \angle{ABD} = 77^{\circ}, BC = CD$  and  $\angle{BCD} =n^{\circ}$  for some positive integer  $n$ . Compute  $n$ .

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