
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 range of the function $f(x)=\lg (ax^{2}-x+ \frac {a}{16})$ is $\mathbb{R}$; and the proposition $q$: $3^{x}-9^{x} < a$ holds for all real numbers $x$, find the range of values for the real number $a$ if the proposition "$p$ and $q$" is false.

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