
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 cube is cut into four pieces by two planes. The first plane is parallel to face ABCD and passes through the midpoint of edge BG. The second plane passes through the midpoints of edges AB, AD, HE, and GH. Determine the ratio of the volumes of the smallest and largest of the four pieces.

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