
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 plane \(\alpha\) are the same, plane \(\alpha\) is called a "median plane" of the polyhedron.
1. How many different median planes does a tetrahedron have?
2. How many different median planes does a parallelepiped have?
3. Given four non-coplanar points in three-dimensional space, how many different parallelepipeds can be formed using these four points as vertices (among the vertices)? Please provide answers to the above questions and explain the reasoning.

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