
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 the sequences $2, 7, 12, \ldots$ and $3, 11, 19, \ldots$ represent two arithmetic progressions. Consider the set $T$ to be the union of the first $3000$ terms of each sequence. Determine how many distinct numbers are in $T$.
A) 5200
B) 5300
C) 5400
D) 5500
E) 5600

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