
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 that the sequence is a monotonically increasing geometric sequence with the first term being $1$ and satisfies that $\left(a_{3}, \frac{5}{3}a_{4},a_{5} \right)$ forms an arithmetic sequence.
(1) Find the general term formula for the sequence $\left{ a_{n} \right}$;
(2) Find the sum of the first $n$ terms, denoted as $S_{n}$, for the sequence $\left\{na_{n}\right\}$.

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