
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 $y^2=4x$, a line passing through the focus $F$ intersects the parabola at points $A$ and $B$ (point $A$ is below the x-axis). Point $A_1$ is symmetric to point $A$ with respect to the x-axis. If the slope of line $AB$ is 1, then find the slope of line $A_1B$.

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