
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
The vertex of the parabola is at the origin, and its focus lies on the positive x-axis. The parabola passes through the point (3, 6).
(1) Determine the length of the chord formed by the intersection of the parabola with the line $y=2x-6$.
(2) Discuss the positional relationship between the line $y=kx+1$ and the parabola, and find the range of values for $k$ that correspond to this relationship.

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