
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 that $M$ is the midpoint of the radius $OP$ of sphere $O$, a plane perpendicular to $OP$ through $M$ intersects the spherical surface to form circle $O_1$. The volume ratio of the sphere with circle $O_1$ as its great circle to sphere $O$ is ______.

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