
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
The set of all solutions of the system 
$$
\begin{cases}
x+y\leq 4 \\
2x+y\geq 1 \\
x\geq 0 \\
y\geq 0
\end{cases}
$$ 
is a quadrilateral region. Find the number of units in the length of the longest side. Express your answer in simplest radical form.

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