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

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