
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 propositions p and q, where proposition p states that the equation $\frac {x^2}{9-2k} + \frac {y^2}{k} = 1$ represents an ellipse with foci on the y-axis, and proposition q states that the equation $\frac {x^2}{2} - \frac {y^2}{k} = 1$ represents a hyperbola with an eccentricity $e$ in the interval $(\sqrt{3}, 2)$. If the conjunction of propositions p and q is false and their disjunction is true, find the range of real values for $k$.

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