
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 alloy with the same mass but different percentage contents of copper, a piece of equal mass was cut from each. Each of the cut pieces was fused with the remaining part of the other piece, after which the percentage content of copper in both pieces became the same. By what factor is the cut piece smaller than the whole piece?

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