
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 $p$: The equation $\frac{x^2}{16 - m} - \frac{y^2}{4 - m} = 1$ represents an ellipse with foci on the $x$-axis.
- Proposition $q$: The point $(m, 4)$ is inside the circle $(x - 10)^2 + (y - 1)^2 = 13$.

Find the range of real values for $m$ if the proposition $p \lor q$ is true and $p \land q$ is false.

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