
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

\[ 
\left\{
\begin{array}{l}
(|y-10|+|x+3|-2)(x^{2}+y^{2}-6)=0 \\
(x+3)^{2}+(y-5)^{2}=a
\end{array}\right.
\]

has exactly three solutions.

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