
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 a sequence $\{a_{n}\}$ that satisfies $a_{1}+2a_{2}+4a_{3}+\ldots +2^{n-1}a_{n}=\frac{n}{2}$, rearrange the sequence $\{a_{n}\}$ into a new sequence as follows: $a_{1}$, $a_{2}$, $a_{2}$, $a_{2}$, $a_{3}$, $a_{3}$, $a_{3}$, $a_{3}$, $a_{3}$, $\ldots$, $\underbrace{{a_n},{a_n},…,{a_n}}_{({2n-1}) terms}$, $\ldots$. Find the sum of the first 70 terms of the new sequence.

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