
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 $f(x)=|3x+ \frac {1}{a}|+3|x-a|$.
- (I) If $a=1$, find the solution set for $f(x)\geqslant 8$;
- (II) For any $a\in(0,+\infty)$, and any $x\in\mathbb{R}$, $f(x)\geqslant m$ always holds, find the maximum value of the real number $m$.

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