
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 domain of the function $f(x) = \lg(ax^2 - x + \frac{1}{16}a)$ is $\mathbb{R}$.
- $q$: The inequality $3^x - 9^x < a$ holds for all $x \in \mathbb{R}$.

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

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