
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 the system of inequalities:
\[
\begin{cases}
5x + 10y \leq 30 \\
2x - y \leq 3 \\
x \cdot y \in \mathbb{N}
\end{cases}
\]
Calculate the maximum value of $x + y$.

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