
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 4 cm. The area of face \(ABC\) is \(20 \mbox{ cm}^2\) and the area of face \(ABD\) is \(16 \mbox{ cm}^2\). These two faces meet each other at a \(45^\circ\) angle. Find the volume of the tetrahedron in \(\mbox{cm}^3\).

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