
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 $2\le |x-3|\le 5$.
A) $x \leq 1 \text{ or } x \geq 5$  
B) $-2 \leq x \leq 8$  
C) $[-2, 1] \cup [5, 8]$  
D) $[1, 5]$  
E) $[-2, 5] \cup [1, 8]$

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