
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
The radius of the rear wheel of a cart is twice that of the front wheel. If the circumference of the front wheel were 5 dm larger, and the rear wheel's circumference were 5 dm smaller, then the front wheel would rotate the same number of times over $150 \mathrm{~m}$ as the rear wheel over $187.5 \mathrm{~m}$. What are the radii of the two wheels?

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