
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 \( EFGH \), edge \( EF \) has length 4 cm. The area of face \( EFG \) is \( 20 \mbox{cm}^2 \) and the area of face \( EFH \) 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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