
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
We have three types of silver and copper castings with weights \(5, 3, 2 \, \mathrm{kg}\). By melting the first two together, we obtain an alloy of fineness 0.760. By melting the first and third together, we obtain an alloy of fineness 0.780. By melting the second and third together, we obtain an alloy of fineness 0.852.

What are the finenesses of the available castings?

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