
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
What is the volume of the region in three-dimensional space defined by the inequalities $|x| \le 1$, $|y| \le 1$, $|z| \le 1$, and $|x| \le 1$, $|y| \le 1$, $|z - 2| \le 1$?

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