
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 $f(x)=ax^{2}+ \frac {1}{x}$ (where $a\in\mathbb{R}$).
(1) Discuss the evenness and oddness of the function $f(x)$ and explain the reasons.
(2) If $a>\frac {1}{2}$, determine the monotonicity of the function $f(x)$ on the interval $[1,+\infty)$, and provide a proof using the definition of function monotonicity.

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