
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 sequence $\{a_n\}$ where all terms are positive, and $a_1=2$, $a_{n+1}-a_n= \frac{4}{a_{n+1}+a_n}$. If the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{a_{n-1}+a_n} \right\}$ is $5$, then $n=\boxed{120}$.

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