
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 the sequence 
$$
\begin{array}{l}
a_{0}=134, a_{1}=150, \\
a_{k+1}=a_{k-1}-\frac{k}{a_{k}} \quad (k=1,2, \cdots, n-1).
\end{array}
$$
determine the value of $n$ for which $a_n = 0$.

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