
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 the system of barycentric coordinates associated with the tetrahedron \(A_{1} A_{2} A_{3} A_{4}\), find the equations of:  
a) the line \(A_{1} A_{2}\);  
b) the plane \(A_{1} A_{2} A_{3}\);  
c) the plane passing through \(A_{3} A_{4}\) parallel to \(A_{1} A_{2}\).

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