
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 the sequence {a<sub>n</sub>}, where a<sub>1</sub> = 3, and for any n ∈ N*, we have $$\frac {a_{n}+a_{n+2}}{2}$$ = a<sub>n+1</sub>.
(1) Let b<sub>n</sub> = a<sub>n+1</sub> - a<sub>n</sub>, determine whether the sequence {b<sub>n</sub>} is an arithmetic sequence or a geometric sequence.
(2) If a<sub>2</sub> = 5, and c<sub>n</sub> = $$\begin{cases} \overset{a_{n},n\text{ is odd}}{2^{a_{n}-1},\text{ is even}}\end{cases}$$, find the sum S<sub>2n</sub> of the first 2n terms of the sequence {c<sub>n</sub>}.

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