
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
Let $a$ be a real number, and consider the proposition $p$: the function $f(x) = (a- \frac{3}{2})^x$ is a decreasing function on $\mathbb{R}$, and the proposition $q$: the solution set of the inequality $(\frac{1}{2})^{|x-1|} \geq a$ is empty.  
(1) If $p$ is true, find the range of values for $a$;  
(2) If $q$ is true, find the range of values for $a$;  
(3) If "p and q" is a false proposition, and "p or q" is a true proposition, find the range of values for $a$.

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