
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 variables $x$ and $y$ satisfy the constraint conditions $\begin{cases}\begin{matrix}x+y-2\geq0 \\\\ x-y-2\leq0 \\\\ y\geq1\\end{matrix} \end{cases}$. The minimum value of the objective function $z=x+3y$ is ( ).

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