
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 $p$: $k^{2}-2k-24\leqslant 0$ and $q$: The equation $\frac {x^{2}}{3-k}+ \frac {y^{2}}{3+k}=1$ represents a hyperbola with foci on the $x$-axis.

(1) If proposition $q$ is true, find the range of values for the real number $k$.

(2) If the proposition "$p\vee q$" is true and "$p\wedge q$" is false, find the range of values for the real number $k$.

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