
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 particle starts at the point $(3,0)$ on the coordinate plane. Define a "move" for the particle as a counterclockwise rotation of $\frac{\pi}{6}$ radians about the origin followed by a translation of $6$ units in the positive x-direction. Find the particle's position after $300$ moves.

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