
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 the sets \( A = \{(x, y) \mid y^2 - x - 1 = 0\} \), \( B = \{(x, y) \mid 4x^2 + 2x - 2y + 5 = 0\} \), and \( C = \{(x, y) \mid y = kx + b\} \), find all non-negative integers \( k \) and \( b \) such that \( (A \cup B) \cap C = \emptyset \).

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