
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 a geometric sequence with $a_1 = 4$, and $2a_2 + a_3 = 60$.  
(1) Find $\{a_n\}$.  
(2) If the sequence $\{b_n\}$ satisfies $b_{n+1} = b_n + a_n$ and $b_1 = a_2 > 0$, find $\{b_n\}$.

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