
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
For $x$ real, solve the inequality $2 \leq |x-3| \leq 5$.
**A)** $-2 \leq x \leq 1$ or $5 \leq x \leq 8$  
**B)** $-3 \leq x \leq 0$ or $6 \leq x \leq 9$  
**C)** $0 \leq x \leq 1$ or $3 \leq x \leq 6$  
**D)** $-1 \leq x \leq 2$ or $4 \leq x \leq 7$

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