
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
Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length $1$, $O$ is the center of the base $A B C D$, and $M$ and $N$ are the midpoints of edges $A_{1} D_{1}$ and $C C_{1}$ respectively, find the volume of the tetrahedron $O-M N B_{1}$.

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