
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 inequality $\left(1+k\right)x\leqslant k^{2}+k+4$, where $x$ and $k$ are real numbers.<br/>$(1)$ If $x=3$, find the solution to the above inequality in terms of $k$;<br/>$(2)$ If the inequality holds for all $k\in \left[-4,+\infty \right)$, determine the range of values for $x$.

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