
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
Consider the graph of a function $y=f(x)$, defined as $f(x) = \frac{x - 2}{x - 1}$. Define another function by $g(x)=f(x+a)$. For what value of $a$ will $g(x)$ be symmetric about the line $y = x + 1$?

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