
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 that the first term of the sequence $\{a_n\}$ is $a_1=2$, and the equation $x^{2019}\cdot\sin x+a_{n+1}\cdot\cos x-3a_n=-2$ has a unique real root, find the sum of the first $n$ terms of the sequence $\{a_n\}$.

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