
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 is initially located at $(5,0)$ on a coordinate plane. A "move" is defined as a counterclockwise rotation of $\frac{\pi}{3}$ radians about the origin followed by a translation of $5$ units in the positive $x$-direction. Determine the particle's position after $120$ moves.

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