
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 factory produces a certain product at a rate of $x$ kilograms per hour ($1 \leqslant x \leqslant 10$). The profit earned per hour is given by $100(5x + 1 - \frac{3}{x})$ yuan.

1. Write an expression for the profit earned after producing the product for $t$ hours ($t \geqslant 0$).
2. Find the range of $x$ such that the profit earned after producing the product for 2 hours is no less than 3000 yuan.

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