
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 the arithmetic sequence $\{a\_n\}$ satisfies $a\_1+a\_2=10$, $a\_4-a\_3=2$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) If the geometric sequence $\{b\_n\}$ satisfies $b\_2=a\_3$, $b\_3=a\_7$, find the general term formula of the sequence $\{b\_n\}$.

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