
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 $1 \times \frac{1}{2}$, $2 \times \frac{1}{4}$, $3 \times \frac{1}{8}$, $4 \times \frac{1}{16}$, …  
(1) Find the general formula for the sequence.  
(2) Find the sum of the first $n$ terms of this sequence.

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