
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 general term $a_n$ is a first-degree function of the term number $n$. Find the general formula for the sequence $\{a_n\}$ and compute $a_{2005}$ and $S_{10}$.

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