
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
In a study of 16 ships, the tonnage range is $[192, 3246]$ (unit: tons), and the number of crew members ranges from 5 to 32. The regression equation of the number of crew members $y$ with respect to tonnage $x$ is $\hat{y}=9.5+0.0062x$,

$(1)$ If the tonnage of two ships differs by $1000$, calculate the average difference in the number of crew members;

$(2)$ Estimate the number of crew members for the ship with the maximum tonnage and the ship with the minimum tonnage.

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