
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
Let $a$, $b$, and $c$ be non-negative real numbers, and they satisfy $3a+2b+c=5$ and $2a+b-3c=1$. Let $m=3a+b-7c$, and denote $x$ as the minimum value of $m$, and $y$ as the maximum value of $m$. Then, find the value of $xy$.

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