
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} 2 & 3 & c\_1 \\\\ 0 & 1 & c\_2 \end{pmatrix}\\) and the solution is \\( \begin{cases} \overset{x=3}{y=5} \end{cases}\\), find the value of \\(c\_1 - c\_2 = \_\_\_\_\_\_ \cdot\\)

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