
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 Emma's model lighthouse has a replica light visible from 30 centimeters, and the original lighthouse is 50 meters tall with its light visible from 30 kilometers, determine the height of the model lighthouse to maintain the proper scale.

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