
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 functions $f(x)=e^{x}$, $g(x)= \frac {a}{2}x+b$ ($a,b\in\mathbb{R}$),  
(1) If $h(x)=f(x)g(x)$, $b=1- \frac {a}{2}$. Find the expression for the maximum value $\varphi(a)$ of $h(x)$ on the interval $[0,1]$;  
(2) If $a=4$, and the equation $f(x)=g(x)$ has exactly two distinct real roots on the interval $[0,2]$, find the range of values for $b$.

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