
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>} with the sum of its first n terms denoted as S<sub>n</sub>, it satisfies the condition a<sub>4</sub>•x<sup>2</sup>\-S<sub>3</sub>•x+2＜0, and the solution set for this inequality is $$( \frac {2}{7}，1)$$.
(1) Find the general term formula for the sequence {a<sub>n</sub>}.
(2) If sequence {c<sub>n</sub>} satisfies $$c_{n}=a_{2n}+2^{a_{n}}$$, find the sum of the first n terms for sequence {c<sub>n</sub}}, denoted as T<sub>n</sub>.

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