
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
The tetrahedron $ABCDE$ has congruent side edges and a volume of one unit. Its base is the rectangle $ABCD$. The tetrahedron is intersected by a plane passing through the edge $BC$, creating a cross-section that intersects the side edges $EA$ and $ED$ at points $A_1$ and $D_1$, respectively. The lines $BA_1$ and $CD_1$ intersect at point $M$. What is the volume of the tetrahedron $EMA_1D_1$ if $EM = 2AB$?

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