
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
Indicate all values of \(a\) for which the system of equations
\[
\left\{
\begin{array}{c}
\log_{|x+3|}(a x+4 a)=2 \log_{|x+3|}(x+y) \\
x+1+\sqrt{x^{2}+2 x+y-4}=0
\end{array}
\right.
\]
has two distinct solutions, and find these solutions for each \(a\).

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