
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 parabola $C: y^2 = 2x$, and two lines $PA$ and $PB$ passing through a point $P(1, \sqrt{2})$ on the parabola $C$ with complementary inclination angles, intersecting the parabola $C$ at points $A$ and $B$ respectively, then the slope of line $AB$ is __________.

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