
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 unit purchased an experimental instrument for 32,000 yuan. Assuming that the instrument is used continuously from the first day it is put into use, the maintenance cost on the nth day is $$\frac{n+49}{10}$$ yuan ($n \in \mathbb{N}^{*}$). If the daily average cost of using this instrument is minimized, then it was used for a total of \_\_\_\_\_\_ days.

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