
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
There are 4 numbers, not all of which are identical. If you take any two of them, the ratio of the sum of these two numbers to the sum of the other two numbers will be the same value \( \mathrm{k} \). Find the value of \( \mathrm{k} \). Provide at least one set of four numbers that satisfies the condition. Describe all possible sets of such numbers and determine their quantity.

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