
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 given tetrahedron, we connect the midpoints of the edges to form a new tetrahedron; we then do the same with the new tetrahedron, and so on. 
a) What sequence do the edges of the successive tetrahedrons form?
b) What sequence do the total surface areas form?
c) What sequence do the volumes of the successive tetrahedrons form?

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