
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 sum of four integers is 36. Adding a certain integer \( n \) to the first number, subtracting \( n \) from the second number, multiplying the third number by \( n \), and dividing the fourth number by \( n \) yields the same result. What are these four numbers, and what is \( n \)?

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