
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 $\{a_{n}\}$ where $a_{1}=1$, and ${a_{n+1}}=\left\{\begin{array}{l}2{a_n}, n=2k-1,\\{a_n}+1, n=2k,\end{array}\right.$ where $k\in N^{*}$, find $a_{2}+a_{4}+a_{6}+\ldots +a_{20}$.

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