
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 curve $\frac{x^{2}}{a-2} - \frac{y^{2}}{6-a} = 1$ is a hyperbola, and the proposition $q$: the function $f(x) = (4-a)^{x}$ is an increasing function on $\mathbb{R}$, and the disjunction $p \vee q$ is true while the conjunction $p \wedge q$ is false. Find the range of values of the real number $a$.

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