
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
Consider the polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis, with both coordinate systems having equal unit lengths. The polar coordinates of point P are $P(2, \frac{\pi}{3})$. Find the polar equation of the line passing through point P and perpendicular to the line defined by the parametric equations $\begin{cases} x=t \\ y=t-1 \end{cases} (t \text{ is the parameter})$.

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