
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 the propositions $p$ and $q$:

- $p$: The solution set of the inequality $a^{x} > 1$ (where $0 < a < 1$ or $a > 1$) is $\{x|x < 0\}$.
- $q$: The domain of the function $y=\lg (ax^{2}-x+a)$ is $\mathbb{R}$.

1. If "$p$ and $q$" is true, find the range of values for the real number $a$.
2. If "$p$ and $q$" is false, but "$p$ or $q$" is true, find the range of values for the real number $a$.

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