
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 {a<sub>n</sub>} where the sum of the first n terms is S<sub>n</sub>, and a<sub>n+1</sub> = 1 + S<sub>n</sub> (n ∈ N<sub>+</sub>), and a<sub>2</sub> = 2a<sub>1</sub>.
(Ⅰ) Find the general term formula for the sequence {a<sub>n</sub>}.
(Ⅱ) If b<sub>n</sub> = a<sub>n</sub>log<sub>2</sub>a<sub>n</sub> + (-1)<sup>n</sup>•n, find the sum of the first n terms, H<sub>n</sub>, for the sequence {b<sub>n</sub>}.

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