
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
The graph of the function \( f(x) = x + \frac{1}{x} \) is denoted as \( C_1 \). The graph \( C_2 \) is the reflection of \( C_1 \) about the point \( A(2,1) \), and it corresponds to the function \( g(x) \).
1. Find the expression of the function \( g(x) \).
2. If the line \( y = b \) intersects \( C_2 \) at exactly one point, find the value of \( b \) and the coordinates of the intersection point.
3. Solve the inequality: \( \log_3 g(x) < \log_3 \frac{9}{2} \).

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