
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 \( a_{0} = 1 \) and \( a_{1} = 2 \), and the recurrence relation:
$$
n(n+1) a_{n+1} = n(n-1) a_{n} - (n-2) a_{n-1}, \quad n = 1, 2, 3, \cdots
$$
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}
user