
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 sequences: the first begins with $3$ and has a common difference of $4$, and the second starts at $5$ and has a common difference of $8$. Define $T$ as the union of the first $3003$ terms of each sequence. Determine the number of distinct numbers in the set $T$.
A) 4404  
B) 4504  
C) 4604  
D) 4704

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