
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 $f(x)=|3x+2|$.
- (I) Solve the inequality $f(x) < 4-|x-1|$;
- (II) Given $m+n=1$ ($m,n > 0$), if $|x-a|-f(x) \leqslant \frac{1}{m}+ \frac{1}{n}$ ($a > 0$) always holds, find the range of the real number $a$.

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