
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 $x$ and $y$ satisfy the system of inequalities
\[
\begin{cases}
2x - y \leqslant 0, \\
x + y \leqslant 3, \\
x \geqslant 0,
\end{cases}
\]
find the maximum value of $2x + y$.

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