
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 a sequence $\{a_{n}\}$ with the first term $a_{1}=\frac{3}{2}$ and the sum of the first $n$ terms as $S_{n}$, satisfying $2a_{n+1}+S_{n}=3$ for $n\in\mathbb{N}^{*}$.  
$(1)$ Find $a_{2}$ and $a_{n}$;  
$(2)$ If $S_{n}$ satisfies $\frac{S_{2n}}{S_{n}}>\frac{64}{63}$, find the maximum value of $n$.

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