
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 be: the domain of $f(x) = \frac{1}{\sqrt{ax^2 - ax + 1}}$ is $\mathbb{R}$; proposition q be: the inequality $3^x - 9^x < a-1$ holds for all positive real numbers $x$.
(1) If proposition p is true, find the range of real numbers $a$.
(2) If both propositions p and q are true, find the range of real numbers $a$.

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