
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
Consider real numbers $x$ and $y$. The inequalities $2 \leq |x-5| \leq 9$ and $y = 3x + 2$ must be satisfied simultaneously. Determine the valid values for $y$ given the constraints on $x$.
**A)** $[-10, 11] \cup [23, 44]$
**B)** $[-10, 44]$
**C)** $[-4, 3] \cup [7, 14]$
**D)** $[-12, 11] \cup [21, 46]$

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