
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 $f(x)=e^{x}(\sin x+\cos x)+a$, $g(x)=(a^{2}-a+10)e^{x}$ ($a\in\mathbb{R}$ and $a$ is a constant).  
(I) If the tangent line of the curve $y=f(x)$ at $(0,f(0))$ passes through the point $(1,2)$, find the value of the real number $a$;  
(II) If there exist real numbers $x_{1}$, $x_{2}\in[0,\pi]$ such that $g(x_{2}) < f(x_{1})+13-e^{\frac {\pi}{2}}$ holds, find the range of values for the real number $a$;  
(III) Determine the number of zeros of the function $\varphi(x)= \frac {b(1+e^{2})g(x)}{(a^{2}-a+10)e^{2}x} - \frac {1}{x}+1+\ln x$ ($b > 1$) on $(0,+\infty)$, and explain the reason.

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