
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 chemical reagent factory in Nantong produces a certain product at a constant speed of $x$ kilograms per hour (the production conditions require $1 \leqslant x \leqslant 10$), and the profit per hour is $5x + 1 - \frac{3}{x}$ thousand yuan.

(1) To make the profit of producing this product for 2 hours not less than 30 thousand yuan, find the range of $x$;

(2) To make the profit of producing 120 kilograms of this product the maximum, what production speed should the factory choose? Also, find this maximum profit.

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