
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
John traveled on his bicycle for five days, with each day's duration ranging from one to five hours, one hour increment per day. His speed allowed him to travel a mile in an integer number of minutes. From the second day onwards, the number of minutes to travel one mile halved from the previous day until it reached a minimum bound, then remained constant for the remaining days. Determine the total number of miles John traveled if the total time to travel one mile for all days is 30 minutes.

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