
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 $f(x)$ defined as follows:
$$
f(x) =
\begin{cases}
a^{x} & \text{if } x < 0 \\
(a - 3)x + 4a & \text{if } x \geq 0
\end{cases}
$$
It is known that for any $x_1 \neq x_2$, the following inequality holds:
$$
\frac{f(x_1) - f(x_2)}{x_1 - x_2} < 0
$$
Find the range of possible values for $a$.

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