
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 variables $x$ and $y$ satisfy the system of inequalities $\begin{cases}x+y\geqslant 3 \\ x-y\geqslant -1 \\ 2x-y\leqslant 3\end{cases}$, then the maximum value of $\dfrac{y}{x}$ is ______.

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