
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
Tourists were pleased with their cook: he prepared a delicious soup during the trip. Revealing the "secrets" of his culinary skills, the young cook disclosed that he took as much water as the combined weight of the grains, potatoes, onions, and fat; as many grains as the combined weight of the potatoes, onions, and fat; as many potatoes as the combined weight of the onions and fat; and fat in half the amount of onions. The total weight of the soup is 12 kg. How much water, grains, potatoes, onions, and fat were used separately for the soup?

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