
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 $\{a_{n}\}$ where $a_{1}=1$ and $a_{2}+a_{3}=5$.<br/>$(Ⅰ)$ Find the general formula for $\{a_{n}\}$;<br/>$(Ⅱ)$ Let $\{b_{n}\}$ be a geometric sequence with $b_{1}=2$ and $b_{3}=2b_{2}$. Determine the sum of the first $n$ terms of the sequence $\{a_{n}+b_{n}\}$ denoted by $T_{n}$.

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