
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 an arithmetic sequence $\left\{ a_n \right\}$ and a geometric sequence $\left\{ b_n \right\}$ satisfy $a_1=b_1=1$, $a_2+a_4=10$, and $b_2b_4=a_5$.

(Ⅰ) Find the general formula for $\left\{ a_n \right\}$;

(Ⅱ) Calculate the sum: $b_1+b_3+b_5+\ldots +b_{2n-1}$.

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