
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
\(ABCD - A_{1}B_{1}C_{1}D_{1}\) is a cube with side length 1. Points \(D, E, F\), and \(G\) are the midpoints of \(BA\), \(BC\), \(BB_{1}\), and \(A_{1}D_{1}\) respectively. What is the volume of the tetrahedron \(G-DEF\)?

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