
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 sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}$, $na_{n+1}-(n+1)a_{n}+1=0$ for $n\in \mathbb{N}^{*}$, and $a_{1}=3$, $a_{2}=5$. If $m>\frac{{S}_{n}}{{2}^{n+1}}$ always holds, then the range of real number $m$ is ______.

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