
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
The function $f(x)= \begin{cases} -(x-a)^{2}-k-a, & x\leqslant a \\ \frac {e^{x}}{a-x}, & x > a\end{cases}$. If there exists $x_{0}\in(-\infty,a]$ such that for all $x_{1}\in(a,+\infty)$, we have $f(x_{1})\leqslant f(x_{0})$, then determine the range of the real number $k$.

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