
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 store purchases a certain number of shirts at a price of $50$ yuan each. In the first month, they sell them at a price of $80$ yuan each and sell 200 pieces. In the second month, in order to increase sales and offer customers a better deal, they decide to reduce the price. After market research, ______, how should they price the shirts to make a profit of $7920 each month in the future?<br/>Solution: Let $\ldots \ldots $<br/>According to the question, we have $\left(80-50-x\right)(200+\frac{x}{2}\times 40)=7920$<br/>$\ldots \ldots $<br/>Based on the equation above, complete the following tasks:<br/>$(1)$ The missing condition in the parentheses in the math problem is ______;<br/>$(2)$ The actual meaning of the unknown $x$ in the equation is ______;<br/>$(3)$ Please write out the complete solution process to solve the math problem above.

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