
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 the parameter \(a\) for which the system of equations

$$
\left\{\begin{array}{l}
(|y+2|+|x-11|-3)\left(x^{2}+y^{2}-13\right)=0 \\
(x-5)^{2}+(y+2)^{2}=a
\end{array}\right.
$$

has exactly three solutions.

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