
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 $a\in\mathbb{R}$, let:

p: the function $f(x)=x^2+(a-1)x$ is an increasing function on the interval $(1, +\infty)$,

q: the equation $x^2-ay^2=1$ represents a hyperbola.

(1) If p is true, find the range of the real number $a$.
(2) If "p and q" are both true, find the range of the real number $a$.

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