
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 certain product in a shopping mall sells an average of 30 items per day, with a profit of 50 yuan per item. In order to reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was found that for each item, for every 1 yuan reduction in price, the mall can sell an additional 2 items per day. Let $x$ represent the price reduction per item. Based on this rule, please answer:<br/>$(1)$ The daily sales volume of the mall increases by ______ items, and the profit per item is ______ yuan (expressed in algebraic expressions containing $x$);<br/>$(2)$ Under the same conditions as above, in normal sales situations, how much should each item be reduced in price so that the mall's daily profit reaches 2100 yuan?

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