
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 the function $$f(x)= \begin{cases} (x-2a)(a-x)，x\leq1 \\ \sqrt {x}+a-1，x>1.\end{cases}$$  
(1) If $a=0$, $x\in[0,4]$, then the range of $f(x)$ is \_\_\_\_\_\_ ;  
(2) If $f(x)$ has exactly three zeros, then the range of values for the real number $a$ is \_\_\_\_\_\_ .

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