
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 $f(x)=\left\{\begin{array}{l}-{x^2}-ax-5, x\leq 1\\ \frac{a}{x}, x>1\end{array}\right.$ satisfies that for all $x_1 \neq x_2$, $\frac{{f(x_2)-f(x_1)}}{{x_2-x_1}}>0$ on $(-\infty, +\infty)$. Find the range of real number $a$______.

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