
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
Given a function $f(x) = \log_a(8 - 2x)$ where $a > 0$ and $a \neq 1$.  
(1) If the inverse function of $f(x)$ is itself, find the value of $a$.  
(2) When $a > 1$, find the maximum value of the function $y = f(x) + f(-x)$.

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