
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 arithmetic sequence {a<sub>n</sub>} and the geometric sequence {b<sub>n</sub>} satisfy a<sub>1</sub>\=b<sub>1</sub>\=1, 2b<sub>2</sub>+b<sub>3</sub>\=0, a<sub>1</sub>+a<sub>3</sub>\=2b<sub>3</sub>, find:

(Ⅰ) The general term formula and the sum of the first n terms S<sub>n</sub> for {a<sub>n</sub>};

(Ⅱ) The value of b<sub>1</sub>\-b<sub>2</sub>+b<sub>3</sub>\-b<sub>4</sub>+…+b<sub>2n-1</sub>\-b<sub>2n</sub>.

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