
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 $f(x)=ax^{3}+bx^{2}+cx+d$ takes extreme values at points $O$ and $A$, where $O$ is the origin and $A$ lies on the curve $y=x^{2}\sin x+x\cos x$, $x\in\left[\frac{\pi}{3},\frac{2\pi}{3}\right]$. Find the maximum value of the slope of the tangent line to the curve $y=f(x)$.

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