
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 two arithmetic progressions: $2, 6, 10, \ldots$ and $5, 14, 23, \ldots$. Let $S$ be the union of the first $1500$ terms of each sequence. Determine how many distinct numbers are in $S$.
A) 2800
B) 2833
C) 2900
D) 2950

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