
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
The sequence 1, 1+2, 1+2+2<sup>2</sup>, 1+2+2<sup>2</sup>+2<sup>3</sup>, …, 1+2+2<sup>2</sup>+…+2<sup>n-1</sup>, … has a sum of the first n terms $S_n > 1020$. What is the minimum value of n?

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