
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
Let proposition p be: A real number $k$ satisfies the equation $\frac{x^2}{k-1} + \frac{y^2}{7-a} = 1$ represents an ellipse with foci on the y-axis;  
Proposition q, a real number $k$ satisfies the equation $(4-k)x^2 + (k-2)y^2 = 1$ does not represent a hyperbola.  
(1) If proposition q is true, find the range of values for $k$;  
(2) If p is a necessary but not sufficient condition for q, find the range of values for the real number $a$.

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