
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 $f(x) = \begin{cases} a^x, & x < 1 \\ (a-3)x+4a, & x \geq 1 \end{cases}$, which satisfies $\frac{f(x\_1) - f(x\_2)}{x\_1 - x\_2} < 0$ for any $x\_1 \neq x\_2$, find the range of values for $a$.

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