
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
Cut equal weights of metal from two alloys weighing 12 kg and 8 kg, respectively, each containing different percentages of copper. Then, mix each cut piece with the remaining alloy it was not cut from, and melt them together. After melting, the two new alloys have equal percentages of copper. Find the weight of the alloy cut from each original alloy in kilograms.

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