
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 $3, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, ...$ consists of $3$’s separated by blocks of $2$’s with $n$ $2$’s in the $n^{th}$ block. Calculate the sum of the first $1024$ terms of this sequence.
A) $4166$
B) $4248$
C) $4303$
D) $4401$

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