
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
For the function $y=x+ \frac {a}{x}$ ($a>0$, $x>0$), it is monotonically decreasing on $(0, \sqrt {a}]$ and monotonically increasing on $[\sqrt {a}, +\infty)$. Because its graph resembles the logo of the famous sports brand Nike, we name this function the "Nike function". Suppose a certain "Nike function" $f(x)$ is defined as $f(x)= \frac {x^{2}+x+a}{x}$ ($a>0$, $x>0$).  
(1) If $a=4$, find the maximum and minimum values of the function $f(x)$ on the interval $[\frac {1}{2}, 3]$.  
(2) If the function is monotonic on the interval $[1, 2]$, determine the range of the real number $a$.

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