
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
Find the set formed by the solutions of the following system of equations for all possible values of the parameter \(a\):

\[
\begin{cases}
a x + y = 2a + 3, \\
x - a y = a + 4.
\end{cases}
\]

(For each value of \(a\), find the solution \((x, y)\) of this system, and all these solutions together constitute the desired set of points on the coordinate plane.)

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