
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
The production cost of a certain product is $50$ yuan per unit, and the original selling price is $65$ yuan. According to market forecasts, the selling price in the first quarter from now will decrease by $10\%$, and then increase by $5\%$ in the second quarter. To keep the sales profit unchanged after half a year, let the average percentage decrease in cost per quarter be $x$, the equation based on the question is ____.

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