
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 factory increases its annual production by $6\%$ in the first year of a five-year plan and by an additional $8\%$ in the second year. Over the next three years, they aim to increase production by the same percentage each year so that the average annual increase over the entire plan equals $10\%$. By what percentage should they increase production annually during the last three years?

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