
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 the real numbers $x$ and $y$ satisfy the constraints $\begin{cases} \begin{matrix} \sqrt{3}x - y + \sqrt{3} \geqslant 0 \\ \sqrt{3}x + y - \sqrt{3} \leqslant 0 \\ \end{matrix} \\ y \geqslant 0 \end{cases}$, determine the value of $(x + y)$ when $\frac{y + 1}{x + 3}$ reaches its maximum value.

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