
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
Suppose $x$ and $y$ satisfy the constraints $\begin{cases} & x\geqslant 0, \\  & y\geqslant x, \\  & 4x+3y\leqslant 12, \end{cases}$ determine the range of values for $\dfrac{x+2y+3}{x+1}$.

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