
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 three non-negative real numbers $x$, $y$, and $z$ satisfying the equations $x + 3y + 2z = 3$ and $3x + 3y + z = 4$, find the minimum and maximum values of $M = 3x - 2y + 4z$.

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