
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, $a\_1=4$, and $2a\_2+a\_3=60$.

(1) Find the general term formula for the sequence $\{a\_n\}$;

(2) If the sequence $\{b\_n\}$ satisfies $b_{n+1}=b\_n+a\_n$, $b\_1=a\_2 > 0$, find the general term formula for the sequence $\{b\_n\}$.

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