
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
Lucas and Sarah set off to a concert 15 miles away. Lucas decided to ride his motorcycle while Sarah took a taxi. Lucas reached the concert in 20 minutes, whereas Sarah arrived in 15 minutes. What is the difference, in miles per hour, between Lucas's and Sarah's average speeds?

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