
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
Dima went to school in the morning, but after walking exactly halfway, he realized he had forgotten his mobile phone at home. Dima estimated (he had an A in mental math) that if he continued walking at the same speed, he would reach school 3 minutes before the bell for the first lesson. However, if he ran back home for the phone and then ran to school, he would arrive 3 minutes after the bell. Dima decided to go back home, but he got tired while running (he had a C in physical education), and so he walked from home to school at his normal walking speed. As a result, he was 15 minutes late for the first lesson! By how many times is the speed at which he runs greater than the speed at which he walks?

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