
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 that the sequence $\{a_n\}$ is an arithmetic sequence with a non-zero common difference, $S_6=60$, and $a_1, a_6, a_{21}$ form a geometric sequence.

(I) Find the general term formula $a_n$ for the sequence $\{a_n\}$.

(II) If sequence $\{b_n\}$ satisfies $b_{n+1}-b_n=a_n (n \in \mathbb{N}_+)$, and $b_1=3$, find the general term formula for sequence $\{b_n\}$.

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