
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 $f(x)=x^{2}+\frac{a}{x}$ ($x\neq 0$, constant $a\in \mathbb{R}$).

    (1) When $a=2$, solve the inequality $f(x)-f(x-1) > 2x-1$;

    (2) Discuss the parity of the function $f(x)$ and explain the reasons.

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