
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 $$f(x)=a\left(x+ \frac {1}{x}\right)-\left|x- \frac {1}{x}\right|$$ (where $a\in\mathbb{R}$),
(Ⅰ) When $a= \frac {1}{2}$, find the intervals where $f(x)$ is monotonic;
(Ⅱ) If $f(x)\geq \frac {1}{2}x$ holds for any $x>0$, find the range of values for $a$.

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