
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
Find the volume of the region given by the inequality
\[
|2x + y + z| + |2x + y - z| + |2x - y + z| + |-2x + y + z| \leq 6
\]
under the condition that \(x, y, z \geq 0\).

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