
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
Factory A produces a certain product at a constant speed of $x$ kilograms per hour (production conditions require $1 \leqslant x \leqslant 10$), and the profit obtained per hour is $100(5x+1- \frac {3}{x})$ yuan.  
$(1)$ To ensure that the profit from producing this product for $2$ hours is not less than $3000$ yuan, find the range of values for $x$;  
$(2)$ To maximize the profit from producing $900$ kilograms of this product, what production speed should Factory A choose? And calculate this maximum profit.

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