
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 $B$ are such that the total number of elements in set $A$ is three times the total number of elements in set $B$. Altogether, there are 4500 elements in the union of $A$ and $B$, and their intersection has 900 elements. What is the total number of elements in set $A$?

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