
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 that the function $g(x) = (a- \frac{3}{2})^x$ is a decreasing function on $\mathbb{R}$, and proposition q be that the function $f(x) = \lg(ax^2 - x + \frac{1}{16}a)$ has the domain $\mathbb{R}$. If the compound statement "p and q" is false and the compound statement "p or q" is true, determine the range of values for the real number $a$.

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