
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 the first term is $a_{1}=1$, and ${a_{n+1}}=\left\{\begin{array}{l}{a_n}+2$, when $n$ is odd, $3{a_n}$, when $n$ is even$\end{array}\right.$, then the sum of the first $2n$ terms of the sequence $\{a_{n}\}$ is ____.

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