
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
Given a circle C: $(x-3)^2+(y-4)^2=4$,  
(Ⅰ) If $a=y-x$, find the maximum and minimum values of $a$;  
(Ⅱ) If circle D has a radius of 3 and its center is on the line $L: x+y-2=0$, and it is externally tangent to circle C, find the equation of circle D.

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