
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 \( f(x)=\frac{2x+3}{x-1} \), the graph of the function \( y=g(x) \) is symmetric with the graph of the function \( y=f^{-1}(x+1) \) with respect to the line \( y=x \). Find \( g(3) \).

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