
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
Given the function $f(x) = \begin{cases} -x^{2}+2ax-2a, &(x\geqslant 1) \\ ax+1, &(x < 1) \end{cases}$, it is known that for any $x\_1\neq x\_2$, the inequality $\frac {f(x\_1)-f(x\_2)}{x\_1-x\_2} < 0$ holds. Determine the range of values for the real number $a$.

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