
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
Matthew invested $100,000$ for 3 years at an annual interest rate of 5% compounded semi-annually. Christina invested $100,000$ for the same period of time, at the same interest rate, but the interest was compounded yearly. Calculate the difference in the amount earned by Matthew's investment as compared to Christina's, to the nearest dollar.

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