
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 $x,y$ satisfy the system of inequalities:
\[
\begin{cases} 
& x-1\geqslant 0 \\
& x-y+1\leqslant 0 \\
& x+y-4\leqslant 0 \\
\end{cases}
\]
Find the minimum value of $\dfrac{x}{y+1}$.

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