
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 sequence $\{a_n\}$ has a sum of its first $n$ terms denoted as $S_n$. The sequence satisfies the conditions $a_1=1$, $a_n>0$, and $$a_{n+1}^2-2a_{n+1}\cdot a_n+a_{n+1}-2a_n=0(n∈\mathbb{N}^*)$$, find $S_{2019}$.

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