
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 real values of $x$ that satisfy the inequality $2\le |x-3|\le 5$ and also $(x-3)^2 \leq 16$.
A) $[-1, 1] \cup [5, 8]$   
B) $[-2, 1] \cup [5, 7]$   
C) $[-2, 1] \cup [5, 8]$   
D) $[-1, 1] \cup [5, 7]$

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