
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
Suppose that \(a, b\), and \(c\) are three numbers with
\[ \begin{aligned}
a + b & = 3 \\
a c + b & = 18 \\
b c + a & = 6
\end{aligned} \]
Solve for the value of \(c\).

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