
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) = 2sin( $\frac {π}{3}x- \frac {π}{6}$) (x∈R).
(I) Find the monotonically decreasing interval of the function f(x);
(II) If the graph of the function (x) is shifted to the right by $\frac {1}{2}$ unit length, the resulting graph corresponds to the function g(x), and when x₁∈(-3,-2), x₂∈(0,1), g(x₁)+g(x₂)=0, find the value of g(x₁-x₂).

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