
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 an arithmetic sequence $\{a_n\}$ where all terms are positive and the common difference is $2$, it is known that $a_2a_4 = 4a_3 + 1$.

(1) Find the general term formula for $\{a_n\}$.

(2) Find the sum of $a_1 + a_3 + a_9 + \ldots + a_{3n}$.

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