
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 $a > 0$, $b > 0$, and $a^{2}+b^{2}= \frac {9}{2}$, if $a+b\leqslant m$ always holds,  
(I) find the minimum value of $m$;  
(II) if $2|x-1|+|x|\geqslant a+b$ always holds for any $a$, $b$, find the range of the real number $x$.

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