
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
A line segment of length $3$, with endpoints $A$ and $B$, moves such that $A$ is on the $x$-axis and $B$ is on the $y$-axis. The moving point $C(x,y)$ satisfies $\overrightarrow{AC}=2\overrightarrow{CB}$. Find the equation of the trajectory of point $C$.

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