
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
Given that \(a\), \(b\), and \(c\) are non-negative numbers satisfying \(3a + 2b + c = 5\) and \(2a + b - 3c = 1\), let \(m = 3a + b - 7c\). If \(x\) is the maximum value of \(m\) and \(y\) is the minimum value of \(m\), what is the value of \(xy\)?

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