
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
Define: For the function $f(x)$, if $f(x_{0})=x_{0}$, then $x_{0}$ is called a "fixed point" of $f(x)$, if $f[f(x_{0})]=x_{0}$, then $x_{0}$ is called a "stable point" of $f(x)$. The sets of "fixed points" and "stable points" of the function $f(x)$ are denoted as $A$ and $B$ respectively, that is $A=\{x|f(x)=x\}$, $B=\{x|f[f(x)]=x\}$. The following properties hold: Property 1: $A\subseteq B$; Property 2: If the function $f(x)$ is monotonically increasing, then $A=B$. Given the function $f(x)=e^{ax}$, $x \gt 0$, $a\neq 0$. (1) Discuss the number of elements in the set $A=\{x|f(x)=x\}$; (2) If the set $B=\{x|f[f(x)]=x\}$ has exactly $1$ element, find the range of values for $a$.

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