
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 $y= \sqrt{mx^{2}-6mx+m+8}$, its domain is $\mathbb{R}$.  
(1) Find the range of real numbers $m$;  
(2) When $m$ changes, if the minimum value of $y$ is $f(m)$, find the range of the function $f(m)$.

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