
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 Gerald the giraffe takes 55 equal steps to walk between consecutive lamp posts, and Patricia the penguin covers the same distance in 15 equal waddles, and the distance between the first lamp post and the 31st lamp post is exactly 3720 feet, find the difference in length between Gerald's step and Patricia's waddle.

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