
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 a parabola $C: y^2=4x$ whose directrix intersects the x-axis at point M, a line $l$ passing through M with a slope of $k$ intersects the parabola $C$ at points A and B (with A between M and B).
(1) Let F be the focus of the parabola $C$. If $|AM| = \frac{5}{4}|AF|$, find the value of $k$.
(2) If there always exists a point Q on the parabola $C$ such that $QA \perp QB$, determine the range of values for $k$.

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