
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
Alexia designed another version of a logo, originally 3 inches wide and 2 inches tall, to be used on her school's event posters. The school wants the logo on the poster to be 12 inches wide. How tall, in inches, will the logo be if it is enlarged proportionately? Additionally, the school also wants a smaller version of the same logo to be 1.5 inches wide for badges. How tall will this smaller logo be?

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