
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
Selected Exercise $(4-5)$: Inequality Lecture

Given that the solution set of the inequality $|x-a| < b$ with respect to $x$ is $\{x|2 < x < 4\}$.

(I) Find the values of the real numbers $a$ and $b$;

(II) Suppose the real numbers $x$, $y$, and $z$ satisfy the equation $\frac{{{(x-b)}^{2}}}{16}+ \frac{{{(y+a-b)}^{2}}}{5}+ \frac{{{(z-a)}^{2}}}{4}=1$, find the maximum and minimum values of $x$, $y$, and $z$.

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