
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
Find all functions \( f: \mathbb{Q} \rightarrow \{-1, 1\} \) such that for all distinct \( x, y \in \mathbb{Q} \) satisfying \( xy = 1 \) or \( x + y \in \{0, 1\} \), we have \( f(x) f(y) = -1 \).

Intermediate question: Let \( f \) be a function having the above property and such that \( f(0) = 1 \). What is \( f\left(\frac{42}{17}\right) \) ?

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