
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 \(ABCD\), \(\angle ADB = \angle BDC = \angle CDA = 60^\circ\). The areas of \(\triangle ADB\), \(\triangle BDC\), and \(\triangle CDA\) are \(\frac{\sqrt{3}}{2}\), \(2\), and \(1\) respectively. What is the volume of the tetrahedron?

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