
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
In the geometric sequence $\left\{ {{a}_{n}} \right\}$, if the common ratio $q=4$, and the sum of the first three terms is equal to $21$,

(1) Find the general term formula of the sequence $\left\{ {{a}_{n}} \right\}$;

(2) Let ${b}_{n}={a}_{n}+2n$, find the sum of the first $n$ terms of the sequence $\left\{ {{b}_{n}} \right\}$, denoted as ${S}_{n}$.

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