
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 the function $f(x)= \begin{cases} x^{3}-x^{2}, & x > 0 \\ axe^{x}, & x\leqslant 0 \end{cases}$, where $a > 0$.  
$(1)$ If the line $y=m$ intersects the graph of the function $f(x)$ only once in the interval $(0,2]$, find the range of values for $m$;  
$(2)$ If $f(x)\geqslant -a$ holds for all $x\in\mathbb{R}$, find the range of values for the real number $a$.

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