
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 $f(x)=2\sin (\omega x+\varphi)$ $(\omega > 0,|\varphi| < \pi)$, the graph of the function passes through the points $\left( \frac{\pi}{12},-2 \right)$ and $\left( \frac{7\pi}{12},2 \right)$, and is monotonic in the interval $\left( \frac{\pi}{12}, \frac{7\pi}{12} \right)$.  
$(1)$ Find the values of $\omega$ and $\varphi$;  
$(2)$ Let $a_{n}=nf\left( \frac{n\pi}{3} \right)$ $(n\in\mathbb{N}^*)$, calculate the sum of the first $30$ terms of the sequence $\{a_{n}\}$, denoted as $S_{30}$.

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