
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 $p$: real number $x$ satisfies $x^2-4ax+3a^2<0$ ($a>0$), and $q$: real number $x$ satisfies $x=\left(\frac{1}{2}\right)^{m-1}$, where $m\in(1,2)$.  
(I) If $a=\frac{1}{4}$ and $p\land q$ is true, find the range of real numbers $x$.  
(II) If $q$ is a sufficient but not necessary condition for $p$, find the range of real numbers $a$.

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