
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
Given condition p: A real number $x$ satisfies $(x-a)(x-3a) < 0$, where $a > 0$; condition q: A real number $x$ satisfies $8 < 2^{x+1} \leq 16$.
(1) If $a=1$, and "p and q" is true, find the range of real numbers $x$;
(2) 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}
user