
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 $\{ a\_n \}$ and geometric sequence $\{ b\_n \}$ that satisfy $a\_1=b\_1=1, a\_2+a\_4=10, b\_2b\_4=a\_5$.

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

(2) Find the sum: $b\_1+b\_3+⋯+b\_{2n−1}$.

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