
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 $p: k^2 - 8k - 20 \leqslant 0$ and $q:$ the equation $\frac{x^2}{4-k} + \frac{y^2}{1-k} = 1$ represents a hyperbola with foci on the $x$-axis.

(1) Find the range of real values of $k$ for which proposition $q$ is true.

(2) If the proposition "$p \lor q$" is true and "$p \land q$" is false, find the range of real values of $k$.

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