
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 $x^2-x-2\leq0$, q: Real number x satisfies $$\frac{x-3}{x}<0$$, r: Real number x satisfies \[x-(a+1)\]\[x+(2a-1)\]\leq0, where $a>0$.
(1) If $p\land q$ is true, find the range of real numbers x.
(2) If p is a sufficient but not necessary condition for r, find the range of real numbers a.

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