
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 $f(x)=\ln (a+x)-\ln (a-x) (a > 0)$.
(I) Find the value of $a$ such that the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$ is $y=2x$.
(II) Find the range of values for $a$ such that $f(x)\geqslant 2x+\dfrac{2{x}^{3}}{3}$ when $x\geqslant 0$.

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