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

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