
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
In the geometric sequence {a<sub>n</sub>} and arithmetic sequence {b<sub>n</sub>}, it is known that a<sub>n</sub> > 0, a<sub>1</sub> = b<sub>1</sub> = 1, a<sub>5</sub> + b<sub>3</sub> = 21, a<sub>3</sub> + b<sub>5</sub> = 13.  
(Ⅰ) Find the general formulas for sequences {a<sub>n</sub>} and {b<sub>n</sub>.}  
(Ⅱ) Find the sum S<sub>n</sub> of the first n terms of the sequence $\left\{\frac{{b}_{n}}{2{a}_{n}}\right\}$.

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