
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
Let $a_{1} = 1, a_{2} = \frac{5}{3}, a_{n+2} = \frac{5}{3} a_{n+1} - \frac{2}{3} a_{n}, (n = 1, 2, \cdots)$.
(1) Let $b_{n} = a_{n+1} - a_{n} (n = 1, 2, \cdots)$. Find the general term formula for the sequence $\left\{ b_{n} \right\}$.
(2) Find the sum of the first $n$ terms $S_{n}$ of the sequence $\left\{ n a_{n} \right\}$.

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