
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 that A(x_{1},y_{1}) and B(x_{2},y_{2}) are two distinct points on the parabola y^{2}=x and are on the same side of the x-axis, with point C(1,0). If the slopes of lines AC and BC are opposite numbers, find the product of y_{1} and y_{2}.

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