
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 that $a > 3$ and $a \neq \frac{7}{2}$, proposition $p$: the exponential function $f(x)=(2a-6)^{x}$ is strictly decreasing on $\mathbb{R}$, proposition $q$: the two real roots of the equation $x^{2}-3ax+2a^{2}+1=0$ with respect to $x$ are both greater than $3$. If $p$ or $q$ is true, and $p$ and $q$ are both false, find the range of values for the real number $a$.

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