
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
The sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=\frac{1}{4}$, $a_{2}=\frac{1}{5}$, and $a_{1} a_{2}+a_{2} a_{3}+\cdots+a_{n} a_{n+1}=n a_{1} a_{n+1}$ for any positive integer $n$. What is the value of $\frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{97}}$?

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