
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 small boat is moving uniformly along a straight line towards a pier. At $0$ minutes, $2$ minutes, $4$ minutes, and $6$ minutes, the distances between the boat and the pier are measured to be $200m$, $150m$, $100m$, and $50m$ respectively.  
$(1)$ The average speed of the boat per minute is ______ $m$;  
$(2)$ Let the distance between the boat and the pier be $y$ (unit: $m$), and the time the boat travels be $x$ (unit: $\min$). Write the analytical expression of $y$ in terms of $x$ and find the range of values for the independent variable $x$.

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