
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:
Proposition $p$: The function $y=a^{x} (a > 0, a \neq 1)$ is a monotonically decreasing function on $\mathbb{R}$.
Proposition $q$: The range of the function $y=\lg (ax^{2}-x+a)$ is $\mathbb{R}$.
If the proposition "$p$ and $q$" is false, find the range of values for $a$.

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