
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 $f\left(x\right)=x^{m}-\dfrac{2}{x}$, and $f\left(4\right)=\dfrac{7}{2}$.
(1) Find the value of $m$;
(2) Determine the parity of $f\left(x\right)$;
(3) Determine the monotonicity of $f\left(x\right)$ on $\left(0,+\infty \right)$, and provide a proof.

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