
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 the spatial rectangular coordinate system O-xyz, there are 8 points: P<sub>1</sub>(1, 1, 1), P<sub>2</sub>(-1, 1, 1), …, P<sub>7</sub>(-1, -1, -1), P<sub>8</sub>(1, -1, -1) (where the x, y, and z coordinates of each point are either 1 or -1). Count the number of tetrahedra that can be formed with any four of these points as vertices.

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