
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 a piece of equal weight from each of two alloys, one weighing 10 kg and the other 15 kg, with different percentages of copper content. Then, melt each cut piece with the remaining part of the other alloy. If the percentages of copper in the two resulting alloys are exactly equal, determine the weight of the piece cut off.

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