
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
During the Dragon Boat Festival, a black pork zongzi workshop in Ding'an County has accumulated a batch of goods and wants to clear the inventory as soon as possible by reducing prices. According to the survey, if each box of black pork zongzi makes a profit of $50, 50 boxes can be sold. For each decrease of $1 in the unit price of each box of black pork zongzi, 2 more boxes can be sold. Let the price reduction for each box of black pork zongzi be $x$.

$(1)$ After reducing the price of each box of black pork zongzi by $x$ dollars, the profit per box of black pork zongzi is ______ dollars, and the number of goods that can be sold is ______ boxes (expressed in algebraic expressions containing $x$).  
$(2)$ If the total profit from selling the goods is to reach $2800, find the value of $x$.

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