
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 an arithmetic sequence $\{a\_n\}$, the first three terms are $a-1$, $4$, $2a$, and the sum of the first $n$ terms is denoted as $S\_n$.
(I) If $S\_k=2550$, find the values of $a$ and $k$;
(II) If $b\_n=\frac{S\_n}{n}$, find the value of $b\_3+b\_7+b\_11+...+b\_{4n-1}$.

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