
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
If the augmented matrix of a system of linear equations is $$\begin{pmatrix} 2 & 3 & c_{1} \\ 3 & 2 & c_{2} \end{pmatrix}$$, and the solution to the system is $$\begin{cases} x=2 \\ y=1 \end{cases}$$, then find the value of $c_{1}-c_{2}$.

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