
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 a right quadrilateral prism \(A B C D-A_{1} B_{1} C_{1} D_{1}\) with edge lengths of 2 and \(\angle B A D=60^{\circ}\), let \(M\) and \(N\) be the midpoints of edges \(C C_{1}\) and \(A B\) respectively. What is the volume of the tetrahedron \(A_{1}-D_{1} M N\)?

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