
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
Given that the actual total volume of a cylindrical tower with a conical roof is 150,000 cubic meters, where the tower is 50 meters tall and the conical roof is 10 meters, and the volume of Alice's scaled model will be 1.5 cubic meters, determine the height of Alice's scaled model.

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