
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
At the start of a cycling trip, you cycle at 15 miles per hour helped by a tailwind. Later, as you turn back against the wind, your effective speed drops to 10 miles per hour due to wind resistance. If you travel a total of 150 miles in 12 hours, for how many hours did you have the help of the tailwind? Express your answer as a common fraction.

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