
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 $f(x)= \frac{e^{x}}{2}- \frac{a}{e^{x}}$, determine the range of the real number $a$ such that for any $x\_1$, $x\_2\in[1,2]$, and $x\_1\neq x\_2$, it satisfies that $[|f(x\_1)|-|f(x\_2)|](x\_1-x\_2) > 0$.

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