
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 $f(x) = mx + \frac{n}{x}$, the equation of the tangent line at the point $(1, a)$ is $3x + y - 8 = 0$.

(Ⅰ) Find the values of the real numbers $m$ and $n$;  
(Ⅱ) Determine the intervals of monotonicity for the function $f(x)$;  
(Ⅲ) Determine the range of values for the angle of inclination $\alpha$ of the tangent line to the function $f(x)$.

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