
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 $p$: The real number $x$ satisfies $\dfrac{x-3a}{a-2x}\geqslant 0$ ($a > 0$); $q$: The real number $x$ satisfies $2x^{2}-7x+6 < 0$.

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

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

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