
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 positive term geometric sequence {a<sub>n</sub>} and the arithmetic sequence {b<sub>n</sub>} satisfy a<sub>1</sub> = b<sub>1</sub> = 1, a<sub>2</sub> + b<sub>2</sub> = 7, and a<sub>2</sub> is the geometric mean of b<sub>1</sub> and b<sub>3</sub> + 2.
(Ⅰ) Find the general term formulas for the sequences {a<sub>n</sub>} and {b<sub>n</sub>}.
(Ⅱ) Let c<sub>n</sub> = (-1)<sup>n</sup>b<sub>n</sub> + a<sub>n</sub>b<sub>2n</sub>, find the sum T<sub>n</sub> of the first n terms of the sequence {c<sub>n</sub>}.

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