
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
Consider the system of inequalities:
$$
\begin{cases}
x + y \leq 5 \\
3x + y \geq 3 \\
x \geq 0 \\
y \geq 0
\end{cases}
$$
This system defines a polygonal region. Determine the number of units in the length of the longest side of this region. Express your answer in simplest radical form.

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