
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 $\frac{x^2}{4-t} + \frac{y^2}{t-1} = 1$ represents an ellipse with foci on the $x$-axis.
- Proposition $q$: The inequality $t^2 - (a+3)t + (a+2) < 0$ with respect to the real number $t$.

1. If proposition $P$ is true, find the range of values for the real number $t$.
2. If proposition $P$ is a sufficient but not necessary condition for proposition $q$, find the range of values for the real number $a$.

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