
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
Given four points A(4, 1, 1), B(4, -2, -1), C(-2, -2, -1), and D(-2, 1, -1) in a rectangular coordinate system. A sphere M passes through these four points. If a point P is randomly chosen from inside the sphere M, the probability that point P is inside the triangular pyramid A-BCD is \_\_\_\_\_\_.

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