
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 propositions $p$: The domain of the function $y=\log(ax^2-ax+1)$ is $\mathbb{R}$, and proposition $q$: The function $y=x^{a^2-2a-3}$ is decreasing on the interval $(0, +\infty)$, if "p OR q" is a true statement, and "p AND q" is a false statement, determine the range of the real number $a$.

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