
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 that the graph of the function \( f(x)=\log_{a}(2+ax) \) and the graph of the function \( g(x)=\log_{\frac{1}{a}}(a+2x) \) (where \( a > 0 \) and \( a \neq 1 \)) are symmetric with respect to the line \( y=b \) (where \( b \) is a constant), find the value of \( a + b \).

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