
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 $f(x)= \frac {x^{2}+2x+a}{x}$, where $x\in[1,+\infty)$,  
(1) If $a= \frac {1}{2}$, find the minimum value of $f(x)$;  
(2) If for any $x\in[1,+\infty)$, $f(x) > 0$ always holds, find the range of the real number $a$.

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