
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 $f(x)=\ln \frac{1+x}{1-x}$,

(1) Find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$;

(2) Determine the maximum value of the real number $k$ such that $f\left(x\right) > k\left(x+ \frac{{x}^{3}}{3}\right)$ holds true for $x\in(0,1)$.

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