
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
Let  $x, y,z$  satisfy the following inequalities  $\begin{cases} | x + 2y - 3z| \le 6 
| x - 2y + 3z|  \le  6  
| x - 2y - 3z|  \le 6 
| x + 2y + 3z|  \le  6 \end{cases}$ Determine the greatest value of  $M = |x| + |y| + |z|$ .

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