
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 the sequence ${a_n}$ with the sum of its first $n$ terms $S_n = k \times 2^n - k$ (where $k$ is a constant) and $a_2 = 4$.

1. Find the value of $k$ and the general term $a_n$;
2. Find the sum of the first $n$ terms, $T_n$, of the sequence ${n a_n}$.

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