
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
The pair \((x, y) = (2, 5)\) is the solution of the system of equations
\[ 
\begin{aligned}
a x + 2 y &= 16 \\
3 x - y &= c
\end{aligned}
\]
Determine the value of \(\frac{a}{c}\).

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