
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) If $f(x) + m \geq 0$ always holds, find the range of $m$.

(2) If the minimum value of $f(x)$ is 6, find the value of $m$.

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