
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
For a plane \(\alpha\), if the distances from all vertices of a polyhedron to \(\alpha\) are equal, then \(\alpha\) is called the "midplane" of the polyhedron.
1. How many distinct midplanes does a tetrahedron have?
2. How many distinct midplanes does a parallelepiped have?
3. Given four non-coplanar points in three-dimensional space, using these four points as vertices (some of the vertices) of a parallelepiped, how many distinct parallelepipeds can be formed?

Please provide the answers to the above questions and explain the reasoning.

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