
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 $f(x)=a\cos x+x^{2}$, where $x\in(-\frac{\pi}{2},\frac{\pi}{2})$, and $a\in R$.
(I) If the slope of the tangent line to the curve $y=f(x)$ at the point $(\frac{\pi}{6},f(\frac{\pi}{6}))$ is $\frac{1}{2}+\frac{\pi}{3}$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$.
(II) If $f(x)\geqslant 2$ always holds true, find the range of values for $a$.

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