
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 $p$ and $q$:
- Proposition $p$: The domain of the function $y = \log_a(x^2 - 2ax + 7a - 6)$ with respect to $x$ is $\mathbb{R}$.
- Proposition $q$: There exists an $x \in \mathbb{R}$ such that the inequality $x^2 - ax + 4 < 0$ holds.
Determine the range of values for $a$ if either proposition $p$ is true and proposition $q$ is false or vice versa.

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