
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
Find the set of $x$-values satisfying the inequality $|\frac{x^2-5x+4}{3}| < 1$.
**A)** $x \in \left[\frac{5 - \sqrt{21}}{2}, \frac{5 + \sqrt{21}}{2}\right]$
**B)** $x \in \left(\frac{5 - \sqrt{21}}{2}, \frac{5 + \sqrt{21}}{2}\right)$
**C)** $x \in \left[\frac{5}{2}, \frac{11}{2}\right]$
**D)** $x \in \left(\frac{11 - \sqrt{21}}{2}, \frac{11 + \sqrt{21}}{2}\right)$
**E)** $x < \frac{5 + \sqrt{21}}{2} \text{ or } x > \frac{5 - \sqrt{21}}{2}$

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