
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 tetrahedron  $ABCD$ , edge  $AB$  has length 3 cm.  The area of face  $ABC$  is 15  $\text{cm}^2$  and the area of face  $ABD$  is 12  $\text{cm}^2$ .  These two faces meet each other at a  $30^\circ$  angle.  Find the volume of the tetrahedron in  $\text{cm}^3$ .

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