
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 proposition $p$: The logarithm $\log_{a}(-2t^{2}+7t-5)$ (where $a > 0$ and $a \neq 1$) is meaningful, and proposition $q$: The inequality about real number $t$, $t^{2}-(a+3)t+(a+2) < 0$.  
$(1)$ If proposition $p$ is true, find the range of values for the real number $t$.  
$(2)$ If proposition $p$ is a sufficient 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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