
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
Given that the variables $x$ and $y$ satisfy the system of inequalities $\begin{cases} & x - 2y + 4 \geqslant 0 \\ & x \leqslant 2 \\ & x + y - 2 \geqslant 0 \end{cases}$, determine the range of values for $\frac{y + 1}{x + 2}$.

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