
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 $C$ and $D$, shown in the Venn diagram, are such that the total number of elements in set $C$ is three times the total number of elements in set $D$. Altogether, there are 4050 elements in the union of $C$ and $D$, and their intersection has 1200 elements. What is the total number of elements in set $C$?

[asy]
label("$C$", (2,67));
label("$D$", (80,67));
draw(Circle((30,45), 22));
draw(Circle((58, 45), 22));
label("1200", (44, 45));
[/asy]

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