
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
Note that when $a=0$, the system is undefined. Suppose the solution of the system is of the form $(x_{0}, x_{0})$. Then we get
$$
\begin{cases}
3x_{0} + 2x_{0} = 15a \\
\frac{1}{a} x_{0} + x_{0} = 9
\end{cases}
$$
that is,
$$
\begin{cases}
5x_{0} = 15a \\
\frac{1+a}{a} \cdot x_{0} = 9
\end{cases}
$$
from which $x_{0} = 3a$. Transforming the second equation of the system by substitution, we get $\frac{1+a}{a} \cdot 3a = 9$. Solving the equation with the restriction that $a \neq 0$, we find $a = 2$. In this case, the solution of the system will be the point $(6, 6)$.

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