
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 $C: y^2 = kx$ ($k > 0$) with focus $F$, and a moving point $N$ on the parabola, the point $M(1, \sqrt{2})$ is not on the parabola.  
(1) If $k=4$, find the minimum value of $|MN| + |NF|$;  
(2) Let $p: 2k^2 - 11k + 5 < 0$, and $q$: the line segment $MF$ intersects the parabola $C$. If $p \land q$ is true, find the range of values for $k$.

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