
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
Points $A$, $B$, $C$, $D$, $E$, and $F$ are located in 3-dimensional space. Points $A$, $B$, and $C$ form a right triangle with $AB=AC=3$, and $\angle BAC = 90^\circ$. Points $D$, $E$, and $F$ form another right triangle with $DE=EF=3$ and $\angle DEF = 90^\circ$. The line $BF$ has a length of 6 and is perpendicular to both triangles at points $B$ and $F$ respectively. What is the volume of the tetrahedron $BCDF$?

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