
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
A vertex of a parallelepiped is $A$, its adjacent vertices are $B$, $C$, and $D$, and the vertex opposite $A$ is $E$. Pass a plane through $E$ that intersects the half-lines $A B$, $A C$, and $A D$. Let the intersection points be denoted by $P$, $Q$, and $R$, respectively.

How should we choose the plane so that the volume of the tetrahedron $A P Q R$ is minimized?

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