
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
Assuming p: The solution set of the inequality $a^x > 1$ is $\{x | x < 0\}$; q: The domain of the function $y= \sqrt{ax^2 - x + a}$ is $\mathbb{R}$. If p or q is a true statement and both p and q are false statements, find the range of the real number $a$.

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