
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
The degree $y$ of myopia glasses is inversely proportional to the focal length $x$ of the lens. It is known that the focal length of myopia glasses with a degree of $400$ is $0.25m$.  
$(1)$ Find the expression for the relationship between $y$ and $x$.  
$(2)$ If Mr. Wang's myopia glasses have a degree of $200$, find the focal length of his glasses.

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