
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: For a real number $x$ satisfying $x^2-4ax+3a^2\leq0$, where $a>0$; proposition q: A real number $x$ satisfies $$\begin{cases} x^{2}-x-6\leq 0 \\ x^{2}+2x-8\geq 0 \end{cases}$$  
(1) If $a=1$ and $p\land q$ is true, find the range of real numbers $x$;  
(2) If $\neg p$ is a sufficient but not necessary condition for $\neg q$, find the range of real numbers $a$.

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