
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 $\{a_n\}$ that satisfies $a_1 + 3a_2 + \cdots + (2n-1)a_n = 2n$.

(1) Find the general formula for the $n^{\text{th}}$ term of the sequence $\{a_n\}$.

(2) Find the sum of the first $n$ terms of the sequence $\{\frac{a_n}{2n+1}\}$.

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