
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
Let $x$ and $y$ satisfy the constraint conditions $\begin{cases}x\geqslant 0 \\ \begin{matrix}y\geqslant x \\ 4x+3y\leqslant 12\end{matrix}\end{cases}$, and $z= \dfrac{x+2y+3}{x+1}$. Determine the range of values of $z$.

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