
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 a sphere O, a plane perpendicular to OP is drawn through M, intersecting the spherical surface to form a circle O<sub>1</sub>. The volume ratio of the sphere with circle O<sub>1</sub> as its great circle to sphere O is \_\_\_\_\_\_.

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