
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 $f(x)=x+ \frac {a}{x}$, where $x\in(0,+\infty)$.  
(I) When $a=1$, use the definition of monotonicity of functions to determine the monotonicity of the function $f(x)$.  
(II) If $x\in[3,+\infty)$, and the inequality $x+ \frac {1}{x}\geqslant |m- \frac {5}{3}|+|m+ \frac {5}{3}|$ always holds for $x$, find the range of the real number $m$.

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