
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 $$f(x)= \begin{cases} a^{x}, x<0 \\ ( \frac {1}{4}-a)x+2a, x\geq0\end{cases}$$ such that for any $x\_1 \neq x\_2$, the inequality $$\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$$ holds true. Determine the range of values for the real number $a$.

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