
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
Let proposition $p$: The real number $x$ satisfies $x^{2}-4ax+3a^{2} < 0$, where $a\neq 0$; proposition $q$: The real number $x$ satisfies $\dfrac{x-3}{2-x}\geqslant 0$.

$(1)$ If $a=1$, and $p\land q$ is a true proposition, find the range of values for $x$;

$(2)$ If $\neg p$ is a sufficient but not necessary condition for $\neg q$, find the range of values for the real number $a$.

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