
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: the first begins with 2 and has a common difference of 3, and the second progression begins with 10 and has a common difference of 7. Let $T$ be the set containing the union of the first $2023$ terms from each sequence. Determine how many distinct numbers are in $T$.
A) 3722
B) 3756
C) 3850
D) 3922
E) 4004

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