
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 the same. If any two of them are taken, the ratio of the sum of these two numbers to the sum of the other two numbers will be equal to the same value k. Find the value of k. Specify at least one set of four numbers that meet the condition. Describe all possible sets of such numbers and determine how many there are.

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