
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 $f(x)=e^{x}$, $g(x)=-x^{2}+2x+b(b\in\mathbb{R})$, denote $h(x)=f(x)- \frac {1}{f(x)}$  
(I) Determine the parity of $h(x)$ and write down the monotonic interval of $h(x)$, no proof required;  
(II) For any $x\in[1,2]$, there exist $x_{1}$, $x_{2}\in[1,2]$ such that $f(x)\leqslant f(x_{1})$, $g(x)\leqslant g(x_{2})$. If $f(x_{1})=g(x_{2})$, find the value of the real number $b$.

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