
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 company has 1000 employees, each generating a profit of 100,000 yuan per year on average. To increase the company's competitiveness, it is decided to optimize the industrial structure by reallocating $x$ ($x \in \mathbb{N}^*$) employees to the tertiary industry. After the adjustment, their average annual profit per person is $10\left(a- \frac{3x}{500}\right)$ ten thousand yuan ($a > 0$), and the average annual profit per person for the remaining employees increases by $0.2x\%$.

$(1)$ To ensure that the total annual profit generated by the remaining employees is not less than the total annual profit generated by the original 1000 employees, what is the maximum number of employees that can be reallocated to the tertiary industry?

$(2)$ Under the condition of $(1)$, if the total annual profit generated by the reallocated employees is always not higher than that generated by the remaining employees, what is the range of values for $a$?

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