
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 $f(x)=x^{2}-mx+m-1$.

1. Find the range of values for the real number $m$ such that $f(x) \geqslant -1$ always holds when $x \in [2,4]$.
2. Determine if there exist integers $a$ and $b$ ($a < b$) such that the solution set of the inequality $a \leqslant f(x) \leqslant b$ with respect to $x$ is $\{x|a \leqslant x \leqslant b\}$. If such integers exist, find their values; otherwise, explain the reason.

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