
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
A cube with an edge length of $10 \text{ cm}$ has one of its edges in the plane of the tabletop, and one of its faces forms a $20^\circ$ angle with the tabletop. The closed cube contains water. Determine the height of the water level from the tabletop to a precision of one tenth of a millimeter when the cube contains a) $0.1$ liters, b) $0.45$ liters, and c) $0.9$ liters of water.

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