
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
An optometrist obtained a set of corresponding data on the degree $y$ of myopia glasses and the focal length $x$ (in meters) as shown in the table below:

| Focal Length $x$ (m) | $1.00$ | $0.50$ | $0.25$ | $0.20$ | $0.10$ |
|----------------------|--------|--------|--------|--------|--------|
| Degree of Myopia $y$ | $100$  | $200$  | $400$  | $500$  | $1000$ |

$(1)$ Please write an appropriate function to describe the relationship between the degree of myopia $y$ and the focal length $x$.

$(2)$ The optometrist measured that Xiaoming's degree of myopia is $250$ degrees. What should be the focal length of the glasses prescribed for Xiaoming?

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