
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 tetrahedron is a polyhedron composed of four triangular faces. Faces  $ABC$  and  $BCD$  of a tetrahedron  $ABCD$  meet at an angle of  $\pi/6$ . The area of triangle  $\triangle ABC$  is  $120$ . The area of triangle  $\triangle BCD$  is  $80$ , and  $BC = 10$ . What is the volume of the tetrahedron? We call the volume of a tetrahedron as one-third the area of it's base times it's height.

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