
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 is a 3 kg alloy of copper and tin, which contains $40 \%$ copper, and another 7 kg alloy of copper and tin, which contains $30 \%$ copper. What masses of these alloys should be taken so that after melting them together, 8 kg of an alloy containing $p \%$ copper is obtained? Find all values of $p$ for which the problem has a solution.

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