
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 solution set of the inequality $a^{x} > 1 (a > 0$ and $a \neq 1)$ with respect to $x$ is $\{x|x < 0\}$, and the proposition $q$: The domain of the function $y = \lg (ax^{2} - x + a)$ is $R$. If the disjunction $p \vee q$ is true and the conjunction $p \wedge q$ is false, then the range of values for the real number $a$ is _______ (blank).

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