
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 side faces of a square-based right pyramid form a $60^{\circ}$ angle with the base. The plane that bisects the angle between the base and one of the side faces divides the pyramid into two parts. Determine the ratio of the volumes of the two parts.

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