
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 the sequence $\{a\_n\}$, where $a\_1=3$, $a\_{10}=21$, and the nth term $a\_n$ is a first-degree function of the term number $n$.
1. Find the general formula for $\{a\_n\}$ and calculate $a\_{2009}$;
2. If $\{b\_n\}$ is a sequence composed of $a\_2$, $a\_4$, $a\_6$, $a\_8$, ..., try to derive a general formula for $\{b\_n\}$.

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