
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 invests a total of $3000, with part of the money at $5\%$ and the remainder at $7\%$. An annual fee of $\18$ is deducted from the interest of the amount invested at $5\%$. If her adjusted annual return from these two investments is the same, calculate the average rate of interest she realizes on the total $3000$.

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