
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 function $f(x)=\frac{1}{2}x^{2}-9\ln x$ is monotonically decreasing in the interval $(m,m+1)$.
- Proposition $q$: The real number $m$ satisfies the equation $\frac{x^{2}}{m-1}+ \frac{y^{2}}{5-m}=1$, representing an ellipse with foci on the $y$-axis.

1. Find the range of values for $m$ when proposition $p$ is true.
2. If the proposition "$p$ and $q$" is false, and the proposition "$p$ or $q$" is true, find the range of values for $m$.

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