
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 $f(x)=(x-a)^{2}\ln x$, where $a\in\mathbb{R}$.
(1) If $a=3 \sqrt {e}$, where $e$ is the base of the natural logarithm, find the monotonic intervals of the function $g(x)= \frac {f(x)}{x}$;
(2) If the function $f(x)$ has both a maximum and a minimum value, find the range of values for the real number $a$.

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