
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
In a three-dimensional Cartesian coordinate system O-xyz, the volume of the spatial region $\Omega_2$ composed of points $(x, y, z)$ satisfying the condition $x^2 + y^2 + z^2 \leq 1$ is denoted as $V_2$ (where $\lfloor x \rfloor$, $\lfloor y \rfloor$, $\lfloor z \rfloor$ represent the greatest integers less than or equal to $x$, $y$, and $z$, respectively). Find $V_2$.

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