
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 functions $f(x)=ax^{3}-x^{2}+x+2$ and $g(x)= \frac {e\ln x}{x}$, for all $x_{1} \in (0,1]$ and $x_{2} \in (0,1]$, find the range of real number $a$ such that $f(x_{1}) \geq g(x_{2})$.

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