
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
Let $1$; $5$; $9$; $\ldots$ and $8$; $15$; $22$; $\ldots$ be two arithmetic progressions. The set $S$ is the union of the first $2100$ terms of each sequence. How many distinct numbers are in $S$?
A) 3800
B) 3900
C) 4000
D) 4100
E) 4200

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