
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 the coordinates of points $M$ and $N$ satisfy the system of inequalities $\left\{\begin{array}{l}x \geqslant 0, \\ y \geqslant 0, \\ x+2 y \leqslant 6, \\ 3 x + y \leqslant 12,\end{array}\right.$ and $\vec{a}=(1,-1)$, find the range of values for $\overrightarrow{M N} \cdot \vec{a}$.

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