
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
Given a tetrahedron $A-BCO$, with $OA$, $OB$, and $OC$ perpendicular to each other and each with the length of 6, a line segment $MN$ with length 2 has one endpoint $M$ moving along the edge $OA$, and the other endpoint $N$ moving inside or on the boundary of the triangle $BCO$. Find the volume of the geometric body formed by the trajectory of the midpoint $R$ of $MN$ and the surfaces of the tetrahedron.

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