
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
Given Hannah cycled 30 miles on her first trip. On a later trip, she cycled 150 miles while going four times faster than her initial speed. Calculate the ratio of her new time compared with the old time.

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