
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 finite sequence $\{a_n\}$ with $k$ terms, and it satisfies $a_{n+1}=a_{n-1}- \frac {n}{a_{n}}$ for $n=2,…,k-1$. If $a_{1}=24$, $a_{2}=51$, and $a_{k}=0$, then $k=$ ______.

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