
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
Donald Duck and Mickey Mouse are competing in a 10,000-meter race. Mickey Mouse runs at a speed of 125 meters per minute, while Donald Duck runs at a speed of 100 meters per minute. Donald Duck has an electronic remote control that can force Mickey Mouse to move backward. When this remote control is used for the \( n \)-th time, Mickey Mouse will move backward for one minute at a speed that is \( n \times 10\% \) of his original speed, then continue running forward at his original speed. What is the minimum number of times Donald Duck needs to use the remote control in order to win the race?

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