
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
$N$ distinct planes intersect a regular tetrahedron $T$. Let $F$ be the union of the faces of $T$, and let $Q =\bigcup_{j=1}^{N}q_{j}$ where $q_j$ are the planes. The intersection of $Q$ and $F$ consists of the union of various line segments joining the vertices to the midpoints of every edge of $T$. Calculate the maximum and minimum values for $N$ and determine the difference between these values.
A) 1   
B) 2   
C) 3   
D) 4   
E) 5

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