
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 $\{a_{n}\}$ that satisfies the following conditions: when $n$ is odd, $a_{n+2}-a_{n}=2$, and when $n$ is even, $2a_{n+2}=a_{n}$.  
$(1)$ If $a_{1}=1$ and $a_{8}=a_{5}$, find $a_{2}$.  
$(2)$ If $a_{1}=1$, $a_{2}=64$, and ${b}_{n}=\frac{1}{64}{a}_{2n}{a}_{2n-1}$, find the sum of the first $n$ terms of the sequence $\{b_{n}\}$ denoted by $S_{n}$.

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