
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 $a_1=3$, $a_{10}=21$, and the general term $a_n$ is a linear function of the index $n$,  
① Find the general formula for $\{a_n\}$ and calculate $a_{2005}$;  
② If $\{b_n\}$ is a sequence formed from $a_2$, $a_4$, $a_6$, $a_8$, ..., deduce a general formula for $\{b_n\}$.

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