
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 $p$: real number $x$ satisfies $x^{2}-4ax+3a^{2}\leqslant 0$, where $a \gt 0$, proposition $q$: real number $x$ satisfies $\left\{\begin{array}{l}{x^2}-x-6＜0\\{x^2}+2x-8＞0\end{array}\right.$. If $\neg p$ is a necessary but not sufficient condition for $q$, then the range of real number $a$ is ______.

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