
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
Let the function $f(x)= \sqrt {x^{2}-3x+2}$ have a domain of set $A$, and the solution set of the inequality $(x-a)(x-3a)\leqslant 0$ be set $B$ (where $a\in\mathbb{R}$, and $a > 0$).  
(I) When $a=1$, find the set $A\cap B$;  
(II) When $A\cap B=B$, find the range of the real number $a$.

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