
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

\[
\begin{cases}
x^2 + (y - a)^2 = 64 \\
(|x| - 6)^2 + (|y| - 8)^2 = 100
\end{cases}
\]

has exactly two solutions.


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