
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 sealed bottle, which contains water, has been constructed by attaching a cylinder of radius \(1 \text{ cm}\) to a cylinder of radius \(3 \text{ cm}\). When the bottle is right side up, the height of the water inside is \(20 \text{ cm}\). When the bottle is upside down, the height of the liquid is \(28 \text{ cm}\). Calculate the total height of the bottle.

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