
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
Consider the sequence ${\{{a}_{n}\}}$ that satisfies ${a}_{1}+3{a}_{2}+\dots +(2n-1){a}_{n}=2n$.

(1) Find the general formula for the sequence ${\{{a}_{n}\}}$;

(2) Calculate the sum of the first $n$ terms of the sequence $\left\{\frac{{a}_{n}}{2n+1}\right\}$.

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