
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
In the sequence $\{a_{n}\}$, $a_{2}=1$, $a_{2k}$, $a_{2k+1}$, $a_{2k+2}(k\in N^{*})$ form a geometric sequence with a common ratio of $q_{k}=\frac{k}{k+1}$. <br/>$(1)$ Calculate $a_{4}$, $a_{6}$, and find $a_{2n}$; <br/>$(2)$ If $a_{1}+a_{3}+a_{5}+\ldots +a_{2n-1} \lt 1$ holds for any $n\in N^{*}$, find the range of values for $a_{1}$.

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