
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
Given that the tetrahedron \(ABCD\) is inscribed in a sphere \(O\), and \(AD\) is the diameter of sphere \(O\), and \(\triangle ABC\) and \(\triangle BCD\) are both equilateral triangles with side length 1, calculate the volume of tetrahedron \(ABCD\).

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