
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
Consider a sequence starting as $1, 2, 1, 2, 2, 1, 2, 2, 2, 1,\ldots$ where each integer $1$ is followed by a block of $2$’s. The difference lies in the new rule where the $n$-th block of $2$’s contains $n!$ (factorial of $n$) instances of $2$. Determine the sum of the first $13$ terms of this sequence.
A) 20
B) 22
C) 24
D) 26
E) 28

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