
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
The area of the shape enclosed by the graph of the function $y=f(x)$, the lines $x=a$, $x=b$, and the x-axis is called the area of the function $f(x)$ on $[a, b]$. It is known that the area of the function $y=\sin nx$ on $[0, \frac{\pi}{n}]$ is $\frac{2}{n}$ ($n\in\mathbb{N}^+$). Then, the area of the function $y=\sin 3x$ on $[0, \frac{2\pi}{3}]$ is $\boxed{\frac{4}{3}}$.

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