
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
What is the value of the sum \( A + B \) if

$$
\frac{1}{A}=1-\frac{1-x}{y}, \quad \frac{1}{B}=1-\frac{y}{1-x}, \quad x=\frac{1-a}{1-\frac{1}{a}}, \quad y=1-\frac{1}{x}
$$

and \( a \neq \pm 1 \)?

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