
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
Define: if m - $$\frac{1}{2}$$ < x ≤ m + $$\frac{1}{2}$$ (where m is an integer), then m is called the nearest integer to the real number x, denoted by {x}, i.e., {x} = m. Based on this, four propositions about the function f(x) = x - {x} are given:
① The domain of y=f(x) is R, and the range is ($$- \frac{1}{2}$$ , $$\frac{1}{2}]$$;
② The point (k, 0) (k ∈ Z) is the center of symmetry for the graph of y = f(x);
③ The least positive period of the function y = f(x) is 1;
④ The function y = f(x) is increasing in the interval ($$- \frac{1}{2}$$ , $$\frac{3}{2}]$$;
Among these, the true propositions are __________.

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