
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  $S_1$  and  $S_2$  be two circles intersecting at points  $A$  and  $B$ . Let  $C$  and  $D$  be points on  $S_1$  and  $S_2$  respectively such that line  $CD$  is tangent to both circles and  $A$  is closer to line  $CD$  than  $B$ . If  $\angle BCA = 52^\circ$  and  $\angle BDA = 32^\circ$ , determine the degree measure of  $\angle CBD$ .

*Ray Li*

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