
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
In the sequence $\{a_n\}$, $a_2=\frac{2}{3}$.

(1) If the sequence $\{a_n\}$ satisfies $2a_n-a_{n+1}=0$, find $a_n$;

(2) If $a_4=\frac{4}{7}$, and the sequence $\{(2n-1)a_n+1\}$ is an arithmetic sequence, find the sum of the first $n$ terms, $T_n$, of the sequence $\left\{\frac{n}{a_n}\right\}$.

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