
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 $f(x) = \log_a(x-1) - 1$ ($a>0$ and $a \neq 1$) passes through a fixed point A, and the line $(m+1)x + (m-1)y - 2m = 0$ passes through a fixed point B, then the equation of the line passing through points A and B is \_\_\_\_\_\_.

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