
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 \( a_{0}=1, a_{1}=2 \), and \( n(n+1) a_{n+1}=n(n-1) a_{n}-(n-2) a_{n-1}, n=1,2,3, \cdots \). Find the value of \( \frac{a_{0}}{a_{1}}+\frac{a_{1}}{a_{2}}+\frac{a_{2}}{a_{3}}+\cdots+\frac{a_{50}}{a_{51}} \).

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