
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
Construct a new sequence $\{a_n\}$ by extracting every 2nd, 4th, 8th, ..., $2^n$th, ... term from the sequence $\{3n+\log_2 n\}$ in the original order. Find the general term $a_n$ for the new sequence $\{a_n\}$ and calculate the sum of the first five terms, $S_5$.

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