
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
Jia and Yi are solving the system of equations simultaneously:
$$
\begin{cases}
& ax+by=2, \\
& cx-3y=-2.
\end{cases}
$$
Jia correctly solves to get
$$
\begin{cases}
& x=1, \\
& y=-1;
\end{cases}
$$
Yi, due to copying the value of $c$ incorrectly, gets the wrong solution
$$
\begin{cases}
& x=2, \\
& y=-6.
\end{cases}
$$
Find the values of $a$, $b$, and $c$.

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