
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 all values of \( a \) for which the system of equations

\[
\left\{\begin{array}{c}\log _{\mid x+3}(a x+4 a)=2 \log _{\mid x+3}(x+y), \\ x+1+\sqrt{x^{2}+2 x+y-4}=0\end{array}\right.
\]

has two distinct solutions, and find these solutions for each \( a \).

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