
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
Find the set of $y$-values satisfying the inequality $3 \leq |y-4| \leq 7$.
**A)** $1 \leq y \leq 4\text{ or }-3 \leq y \leq -7$\
**B)** $11 \leq y \leq 15\text{ or }1 \leq y \leq -3$\
**C)** $7 \leq y \leq 11\text{ or }-7 \leq y \leq -3$\
**D)** $7 \leq y \leq 11\text{ or }-3 \leq y \leq 1$\
**E)** $4 \leq y \leq 8\text{ or }-1 \leq y \leq 3$

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