
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
A sequence $\{a_n\}$ satisfies: $a_1= \dfrac{1}{4}$, $a_2= \dfrac{1}{5}$, and $a_1a_2+a_2a_3+\ldots+a_na_{n+1}=na_1a_{n+1}$ for any positive integer $n$. Find the value of $\dfrac{1}{a_1}+ \dfrac{1}{a_2}+\ldots+ \dfrac{1}{a_{97}}$.

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