
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
Let $f(x)=e^{x}+x-a$ ($a\in\mathbb{R}$, $e$ is the base of natural logarithms).

(I) When $x\in[0,1]$, $f(x)\geqslant 0$ always holds. Find the range of values for $a$.

(II) For the function $g(x)= \sqrt {f(x)}$, if there exists a point $(x_{0},y_{0})$ on the curve $y=\cos 2x$ such that $g(g(y_{0}))=y_{0}$, find the range of values for $a$.

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