
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 $6000$ invested, part at $3\%$ and the rest at $7\%$. If her annual returns from both parts are the same, what is the average rate of interest she realizes on her total investment?
**A)** $3.6\%$
**B)** $4.2\%$
**C)** $5.4\%$
**D)** $6.0\%$
**E)** none of these

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