
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 $f(x) = x - \frac{4}{x}$.

(1) Determine the odd-even nature of the function $f(x)$ and provide a proof.
(2) Determine the monotonicity of the function $f(x)$ in the interval $(0,+\infty)$ and provide a proof.
(3) Find the maximum and minimum values of the function $f(x)$ in the interval $[1,4]$.

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