
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 functions $f(x)=|3x-1|+|3x+k|$ and $g(x)=x+4$,
(Ⅰ) when $k=-3$, find the solution set of the inequality $f(x) \geqslant 4$;
(Ⅱ) let $k > -1$, and for all $x \in \left[ -\frac{k}{3}, \frac{1}{3} \right)$, $f(x) \leqslant g(x)$. Determine the range of values for $k$.

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