
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
Distinct lines $l_1, l_2, ..., l_m$ intersect the interior of a regular tetrahedron T. Let $S'$ be the union of the faces of T and let $L = \bigcup_{i=1}^{m} l_i$. Each line $l_i$ intersects the edges of $T$ precisely at their midpoints. What is the difference between the maximum and minimum possible values of $m$?
A) 0
B) 1
C) 2
D) 3
E) 4

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