
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 a function $y = f(x)$ ($x \in \mathbb{R}$), the slope of the tangent line at any point $(x_0, f(x_0))$ is $k = (x_0 - 3)(x_0 + 1)^2$. Find the interval where the function is monotonically decreasing.

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