
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

$$
\left\{
\begin{array}{c}
(a y-a x+2)(4 y-3|x-a|-x+5 a)=0 \\
\left(\log _{a} x^{2}+\log _{a} y^{2}-2\right) \log _{2} a^{2}=8
\end{array}
\right.
$$

has six distinct solutions.

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