
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 $x^{2}-4ax+3a^{2} < 0$, where $a > 0$, $q$: The real number $x$ satisfies $\begin{cases} x^{2}-x-6\leqslant 0 \\ x^{2}+3x-10 > 0\end{cases}$.
$(1)$ If $a=1$ and $p\land q$ is true, find the range of the real number $x$;
$(2)$ If $\lnot p$ is a sufficient but not necessary condition for $\lnot q$, find the range of the real number $a$.

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