
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 $f(x)$, $(x \in \mathbb{R})$, the equation of the tangent line at any point $(x_{0},y_{0})$ is $y-y_{0}=(x_{0}-2)(x_{0}^{2}-1)(x-x_{0})$. Determine the interval where the function $f(x)$ is monotonically decreasing.

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