
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
According to market research, the cumulative demand for a certain household product from the beginning of the year to the $n$th month approximately satisfies the relationship $S_{n}($in ten thousand units$) = \frac{n}{90}(21n - n^{2} - 5)$, where $n = 1, 2, \ldots, 12$. Based on this prediction, the months in the current year where the demand exceeds 15,000 units are ______.

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