
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 that $a_n > 0$ ($n\in\mathbb{N}^*$), 

(1) If $a_1+a_2=1$, then $\dfrac{1}{a_1}+ \dfrac{1}{a_2} =(a_1+a_2)( \dfrac{1}{a_1}+ \dfrac{1}{a_2}) \geqslant 4$;

(2) If $a_1+a_2+a_3=1$, then $\dfrac{1}{a_1}+ \dfrac{1}{a_2}+ \dfrac{1}{a_3} =(a_1+a_2+a_3)( \dfrac{1}{a_1}+ \dfrac{1}{a_2}+ \dfrac{1}{a_3})\geqslant 9$,

By analogy with (1) and (2), if $a_1+a_2+a_3+a_4=1$, then $\dfrac{1}{a_1}+ \dfrac{1}{a_2}+ \dfrac{1}{a_3}+ \dfrac{1}{a_4} \geqslant$ .

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