
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 $f(x)=|ax-b|+|x+c|$,

(I) When $a=c=3$, $b=1$, find the solution set of the inequality $f(x)\geqslant 4$;

(II) If $a=1$, $c > 0$, $b > 0$, $f(x)_{\min}=1$, find the minimum value of $\frac{1}{b}+\frac{1}{c}$.

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