
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 $f\left(x\right)=\left\{\begin{array}{l}{-{x}^{2}-ax-5, x\leq 1}\\{\frac{a}{x}, x>1}\end{array}\right.$ satisfies $\frac{f({x}_{1})-f({x}_{2})}{{x}_{1}-{x}_{2}} \gt 0$ for any $x_{1}\neq x_{2}$. Find the range of values for $a$.

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