
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
There are three alloys consisting of nickel, copper, and manganese. The first alloy contains $30\%$ nickel and $70\%$ copper. The second alloy contains $10\%$ copper and $90\%$ manganese. The third alloy contains $15\%$ nickel, $25\%$ copper, and $60\%$ manganese. We need to create a new alloy of these three metals that contains $40\%$ manganese. What possible values can the percentage of copper in the new alloy take?

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