
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 $\begin{cases} x=-3 \\ y=-2\end{cases}$ is the solution to the system of equations $\begin{cases} ax+cy=1 \\ cx-by=2\end{cases}$, find the relationship between $a$ and $b$.

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