
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
Sets $A$ and $B$, shown in the Venn diagram, have properties such that the total number of elements in set $A$ is thrice the total number of elements in set $B$. The total number of elements in the union of $A$ and $B$ is 5000, and their intersection has 1000 elements. Determine the total number of elements in set $A$.

[asy]
label("$A$", (2,67));
label("$B$", (80,67));
draw(Circle((30,45), 22));
draw(Circle((58, 45), 22));
label("1000", (44, 45));
[/asy]

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