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

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