
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]


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Given the function $f(x)=2x+1$, the sequence ${{a_{n}}}$ satisfies ${{a_{1}}=1}$, ${{a_{n+1}}=f({a_{n}})-1(n\in {{N}^{\*}}})$, and the sequence ${{b_{n}}}$ is an arithmetic sequence with first term ${{b_{1}}=1}$ and common difference $2$.

(1) Find the general term formulas for the sequences ${{a_{n}}}$ and ${{b_{n}}}$.

(2) Let ${{c_{n}}={{a_{n}}+{{b_{n}}}(n\in {{N}^{\*}})}}$, find the sum of the first $n$ terms of the sequence ${{c_{n}}}$ denoted as ${{T_{n}}}$.

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