
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
Jose invested \$50,000 for 2 years at an annual interest rate of 5 percent compounded yearly. Patricia invested \$50,000 for the same period of time, at the same interest rate, but the interest was compounded monthly. To the nearest dollar, how much more money did Patricia's investment earn than that of Jose?

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