
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 $f(x)=ax+\frac{a}{x}$, $g(x)=e^{x}-3ax$, where $a > 0$, if for all $x\_1\in(0,1)$, there exists $x\_2\in(1,+\infty)$ such that the equation $f(x\_1)=g(x\_2)$ always has a solution, then the range of the real number $a$ is \_\_\_\_\_\_.

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