
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
Let S<sub>n</sub> be the sum of the first n terms of the arithmetic sequence {a<sub>n</sub>}, such that a<sub>2</sub>\=5, S<sub>5</sub>\=35, and T<sub>n</sub> be the sum of the first n terms of the sequence {b<sub>n</sub>}, such that T<sub>n</sub>\=2b<sub>n</sub>\-1 (n∈N<sup>\*</sup>).
(Ⅰ) Find the general term formulas for the sequences {a<sub>n</sub>} and {b<sub>n</sub>}.
(Ⅱ) Let $$c_{n}= \begin{cases} \frac {2}{S_{n}}，n=2k-1 \\ a_{n}b_{n}，n=2k\end{cases}(k∈N^{*})$$, and let P<sub>n</sub> be the sum of the first n terms of the sequence {c<sub>n</sub>}. Find the expression for P<sub>2n</sub>.

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