
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 function $y=\log_{a-1}[(a-3)x-1]$ is increasing in its domain, and proposition q: The function $y=\ln[(3a-4)x^2-2ax+2]$ has the domain of $\mathbb{R}$.
(1) If the proposition "p∨q" is true, find the range of the real number $a$.
(2) If the proposition "p∨q" is true, and "p∧q" is false, find the range of the real number $a$.

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