
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
Determine the set of $x$-values satisfying the inequality $3 \leq |(x-3)^2-4| \leq 7$.
**A)** $3-\sqrt{11} \leq x \leq 3+\sqrt{11}$  
**B)** $3-\sqrt{7} \leq x \leq 3+\sqrt{7}$  
**C)** $x \leq 3-\sqrt{11} \text{ or } x \geq 3+\sqrt{11}$  
**D)** $x \leq 3-\sqrt{7} \text{ or } x \geq 3+\sqrt{7}$

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