
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 $A(-3,0)$ and $B(3,0)$ be two fixed points. If the ratio of the distance from a moving point $P$ to point $A$ and to point $B$ is $1:2$, then the area enclosed by the trajectory of point $P$ is ______.

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