
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 the propositions $p:$ the function $f(x)={(a-\frac{3}{2})}^{x}$ is a decreasing function on $\mathbb{R}$, and $q:$ the function $f(x) ={x}^{2}-4x+3 $ has a range of $\left[-1,3\right] $ on the domain $\left[0,a\right] $. If the proposition "$p\wedge q$" is false and "$p\vee q$" is true, find the range of values for $a$.

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