
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 $f(x)=\log _{3}(1+x)-\log _{3}(1-x)$.
(1) Determine the evenness or oddness of the function $f(x)$ and provide a proof.
(2) Given the function $g(x)=\log _{\sqrt {3}} \frac {1+x}{k}$, find the range of $k$ such that the inequality $f(x)\geqslant g(x)$ holds when $x\in[\frac {1}{3}, \frac {1}{2}]$.

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