
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 Penelope takes 50 equal waddles to walk between consecutive telephone poles, and Hector takes 15 equal jumps to cover the same distance, and the 51st pole is 6336 feet from the first pole, calculate how much longer Hector's jump is than Penelope's waddle.

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