
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 a system of linear equations is \\( \begin{pmatrix} \left.\begin{matrix}2 & 3 & c\_1 \\ 3 & 2 & c\_2\end{matrix}\right. \end{pmatrix}\\), and the solution is \\( \begin{cases}x=2 \\ y=1\end{cases}\\), find the value of \\(c\_1 - c\_2 = \_\_\_\_\_\_ \\).

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