
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
Let $x$ and $y$ be variables that satisfy the following constraints:
\begin{cases}
\begin{matrix}
x - 1 \geqslant 0 \\
x - y \geqslant 0
\end{matrix} \\
x + y - 4 \leqslant 0
\end{cases}
Find the maximum value of $\frac{y}{x}$.

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