
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 $\{a_{n}\}$ is an arithmetic sequence, the sum of the first $n$ terms of the sequence $\{b_{n}\}$ is $S_{n}$, $2a_{1}=b_{1}=2$, $a_{2}+a_{8}=10$, _____. Choose one of the two conditions, either (1) $\frac{1}{2}{S_n}={b_n}-1$, or (2) ${b_n}={2^{λ{a_n}}}$, to fill in the blank above, and complete the solution to the following questions accordingly (if multiple conditions are chosen, answer each separately, scoring according to the first answer). Find the general formulas for sequences $\{a_{n}\}$ and $\{b_{n}\}$; Calculate the sum $T_{n}$ of the first $n$ terms of the sequence $\{a_{n}+b_{n}\}$.

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