
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
Proposition $p$: The line $y=kx+3$ intersects the circle $x^{2}+y^{2}=1$ at points $A$ and $B$; Proposition $q$: The curve $\frac{x^{2}}{k-6} - \frac{y^{2}}{k}=1$ represents a hyperbola with foci on the $y$-axis. If the proposition $p \wedge q$ is true, find the range of values for the real number $k$.

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