
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 $C: y^2 = 4x$, and a line passing through point $A(-1,0)$ with slope $k$ intersects $C$ at points $M$ and $N$. If the midpoint of segment $MN$ lies on the line $x = 3$, then $k = \boxed{\pm 2}$.

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