
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
Knowing the edges of a tetrahedron, its volume can be calculated by determining the height of any vertex. Perform the calculation for the following example: the edge lengths of tetrahedron $ABCD$ are as follows: $AB=6$, $AC=7$, $AD=8$, $CD=9$, $BD=10$, $BC=11$ units. (We can choose the base, for example, the triangle $ABC$.)

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