
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 the functions
$$
\begin{array}{l}
f(x)=\log _{a}(2+a x), \\
g(x)=\log _{\frac{1}{a}}(a+2 x)(a>0, a \neq 1)
\end{array}
$$

whose graphs are symmetric about the line \( y=b \) (where \( b \) is a constant), find the value of
$$
a+b=
$$

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