
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  ${a_0, a_1, a_2, ...}$  of real numbers satisfies the recursive relation   $$ n(n+1)a_{n+1}+(n-2)a_{n-1} = n(n-1)a_n $$   for every positive integer  $n$ , where  $a_0 = a_1 = 1$ . Calculate the sum   $$ \frac{a_0}{a_1} + \frac{a_1}{a_2} + ... + \frac{a_{2008}}{a_{2009}} $$  .

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