
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 $f(x)= \frac{x^{2}+3}{x-m}$ ($m\in\mathbb{R}$, $x > m$).
(1) Find the range of $m$ such that $f(x)+m\geqslant 0$ always holds;
(2) Find the value of $m$ such that the minimum value of $f(x)$ is $6$.

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