
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
In a three-dimensional Cartesian coordinate system, determine the number of lines that pass through four different points of the form \((i, j, k)\) (where \(i, j, k\) are positive integers not exceeding 4).

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