
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 the augmented matrix of the system of linear equations with two variables $$\begin{cases} a_{1}x+b_{1}y=c_{1} \\ a_{2}x+b_{2}y=c_{2}\end{cases}$$ is $$\begin{pmatrix} 1 & -1 & 1 \\ 1 & 1 & 3\end{pmatrix},$$ find the solution for this system.

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