
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 vectors $a=(2,-n)$ and $b=(S_n, n+1)$, where $S_n$ is the sum of the first $n$ terms of the sequence ${a_n}$, and $a$ is perpendicular to $b$. If $n$ is a positive integer, find the maximum value of the term in the sequence ${\frac{a_n}{a_{n+1}a_{n+4}}}$.

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