
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
The vertices $A, B, C, D, A_1, B_1, C_1, D_1$ form a unit cube. The midpoint of edge $BC$ is $F$, and the center of the square $DCC_1D_1$ is $O$. The plane of triangle $AFO$ splits the cube into two solids. Determine the volume ratio of these two solids.

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