
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
Consider tetrahedron $ABCD$ with vertices $A(0, 0, 0),$ $B(1, 0, 0),$ $C(0, 1, 0),$ and $D(0, 0, 1).$ Plane $\pi$ passes through point $M$ (midpoint of edge $AB$), point $N$ (midpoint of edge $CD$), and vertex $A.$ Calculate the volume of the larger part of the tetrahedron where the plane $\pi$ divides it.

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