
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 $3 \leq |x+3| \leq 7$.
**A)** $-10 \leq x \leq -6 \text{ or } 0 \leq x \leq 4$  
**B)** $-4 \leq x \leq 6$  
**C)** $x \leq -6 \text{ or } x \geq 0$  
**D)** $-6 \leq x \leq 10$  
**E)** $-3 \leq x \leq 7$

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