
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 $p$: The domain of the function $f(x)=\lg (ax^{2}-x+ \dfrac {1}{4}a)$ is $\mathbb{R}$; proposition $q$: The inequality $3^{x}-9^{x} < a$ holds for all positive real numbers $x$. If "proposition $p$ or proposition $q$" is true, and "proposition $p$ and proposition $q$" is false, find the range of the real number $a$.

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