
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

\[
\left\{
\begin{array}{l}
x = |y - \sqrt{a}| + \sqrt{a} - 4 \\
(|x| - 6)^2 + (|y| - 8)^2 = 100
\end{array}
\right.
\]

has exactly three solutions.

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