
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
A woman has $5000$ invested in two different schemes, part of it at $3\%$ and the rest at $5\%$. If she earns the same annual return from both parts, find the average rate of interest she realizes on her $5000$ investment.
A) $3\%$
B) $3.75\%$
C) $4\%$
D) $5\%$
E) None of these

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