
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 that set A is the domain of the function $g(x) = \log_a[-(x-2a)(x-a)]$ ($a>0$, and $a \neq 1$), and sets B and C are respectively the domain and range of the function $$f(x)= \sqrt {9-3^{x}}$$.  
(1) Find sets A, B, C;  
(2) If $A \cup C = C$, find the range of the real number $a$.

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