
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 $q$:
- Proposition $p$: $\frac{x^2}{k} + \frac{y^2}{4 - k} = 1$ represents an ellipse with foci on the $x$-axis.
- Proposition $q$: $\frac{x^2}{k - 1} + \frac{y^2}{k - 3} = 1$ represents a hyperbola.

The disjunction $p \vee q$ is true. Find the range of $k$.

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