
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 proposition $p$: The function $g(x)=(a-\frac{3}{2})^x$ is a decreasing function on $\mathbb{R}$, and the proposition $q$: The domain of the function $f(x)=\log_{10}(ax^2-x+\frac{1}{16}a)$ is $\mathbb{R}$. If the statement "$p$ and $q$" is false, and the statement "$p$ 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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