
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
Let the function $f(x)$ be defined on $(0,+\infty)$ with its derivative denoted as $f'(x)$, and it satisfies $x^{4}f'(x)+3x^{3}f(x)=e^{x}$, $f(3)=\dfrac{e^{3}}{81}$. For $x > 0$, regarding the extremum of $f(x)$, the correct statement among the following is ____(fill in the serial number).

① There is a maximum value, no minimum value;

② There is a minimum value, no maximum value;

③ There is neither a maximum nor a minimum value;

④ There is both a maximum and a minimum value.

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