
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 $$f(x)=3 \sqrt {2}cosx\cdot (cosx+sinx)- \frac {3 \sqrt {2}}{2}(x∈R)$$, suppose points P<sub>1</sub>（x<sub>1</sub>，y<sub>1</sub>），P<sub>2</sub>（x<sub>2</sub>，y<sub>2</sub>），…，P<sub>n</sub>（x<sub>n</sub>，y<sub>n</sub>），… are all on the graph of the function y=f（x）, and satisfy $$x_{1}= \frac {π}{6}$$, $$x_{n+1}-x_{n}= \frac {π}{4}(n∈N^{*})$$. Find the value of y<sub>1</sub>+y<sub>2</sub>+…+y<sub>2019</sub>.

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