
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
Given the bookstore purchased a novel twice, once for $500$ yuan and once for $700$ yuan, where the quantity purchased in the second purchase was $4$ more than the first purchase, and the purchase prices were the same, derive the equation that represents the situation in terms of the quantity purchased in the first purchase, $x$.

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