
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
In a tetrahedron \(ABCD\), the angle between faces \(ABC\) and \(BCD\) is \(30^{\circ}\), the area of \(\triangle ABC\) is \(120\), the area of \(\triangle BCD\) is \(80\), and \(BC = 10\). Find the volume of this tetrahedron.

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