
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 $f(x)= \sqrt {3}|\cos \frac {π}{2}x|(x≥0)$, the highest points of the graph from left to right are consecutively labeled as P₁, P₃, P₅, …, and the intersection points of the function y=f(x) with the x-axis from left to right are consecutively labeled as P₂, P₄, P₆, …, Let Sₙ = $\overrightarrow {P_{1}P_{2}}\cdot \overrightarrow {P_{2}P_{3}}+ ( \overrightarrow {P_{2}P_{3}}\cdot \overrightarrow {P_{3}P_{4}})^{2}$+$( \overrightarrow {P_{3}P_{4}}\cdot \overrightarrow {P_{4}P_{5}})^{3}$+$( \overrightarrow {P_{4}P_{5}}\cdot \overrightarrow {P_{5}P_{6}})^{4}$+…+$( \overrightarrow {P_{n}P_{n+1}}\cdot \overrightarrow {p_{n+1}p_{n+2}})^{n}$, then $\overset{lim}{n\rightarrow \infty } \frac {S_{n}}{1+(-2)^{n}}$= \_\_\_\_\_\_.

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