
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: The real number $x$ satisfies $(x-a)(x-3a)<0$, where $a>0$; proposition q: The number $x$ satisfies $2\leq x \leq 3$.
(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}
user