
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
Solve the system of equations $\left\{\begin{array}{}ax+by=2 \\ cx-7y=8\end{array}\right.$. A student mistakenly took $c$ as $-2$ and obtained $\left\{\begin{array}{}x=-2 \\ y=2\end{array}\right.$, while the correct solution is $\left\{\begin{array}{}x=3 \\ y=-2\end{array}\right.$. Find the values of $a$, $b$, and $c$.

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