
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
Below is a portion of the graph of a function, \(y=f(x)\):

\[ \text{[A graph depicting a function symmetric about the line } y = x + 1 \text{ is implied but not shown]} \]

Suppose we define another function by \(g(x) = f(x + b)\). On the evidence of the graph above, for what choice of \(b\) is it true that \(g(x)\) is identical to its inverse, \(g^{-1}(x)\)?

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