
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 domain of the function $f(x) = \log(ax^2 - x + \frac{1}{16}a)$ is $\mathbb{R}$; and the proposition $q$: The function $f(x) = (a - \frac{3}{2})$ is a decreasing function on $\mathbb{R}$. If either proposition $p$ or $q$ is true, and both $p$ and $q$ cannot be true simultaneously, find the range of values for the real number $a$.

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