
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
What is the limit of the following sequence?

$$
a_{n}=\frac{1}{n^{2}}\left[\sin \frac{\pi}{n}+2 \sin \frac{2 \pi}{n}+3 \sin \frac{3 \pi}{n}+\ldots+(n-1) \sin \frac{(n-1) \pi}{n}\right]
$$

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