
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 ${a_{n+1}}=\left\{{\begin{array}{l}{{a_n}+1, n \text{ is odd}}\\{{a_n}+2, n \text{ is even}}\end{array}}\right.$, let $b_{n}=a_{2n}$. Find $b_{1}=$____ and $b_{n}=$____.

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