
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
From two pieces of alloys (with different lead contents) weighing 6 kg and 12 kg, respectively, equal-mass pieces were cut off. Each of the cut pieces was fused with the remainder of the other piece, after which the percentage of lead in both resulting alloys became identical. What are the masses of each of the cut pieces?

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