
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
Faces  $ABC$  and  $BCD$  of tetrahedron  $ABCD$  meet at an angle of  $30^\circ$ . The area of face  $ABC$  is  $120$ , the area of face  $BCD$  is  $80$ , and  $BC=10$ . Find the volume of the tetrahedron.

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