
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
In the rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=3-\frac{\sqrt{2}}{2}t \\ y=1+\frac{\sqrt{2}}{2}t \end{cases}$ ($t$ is a parameter). Establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis. The polar equation of curve $C$ is given by $\rho = 2\cos\left(\theta - \frac{\pi}{6}\right)$.
1. Find the polar equation of line $l$.
2. If line $\theta = \frac{\pi}{3}\ (\rho > 0)$ intersects line $l$ at point $P$ and intersects curve $C$ at point $Q$ ($Q$ does not coincide with the origin $O$), find the value of $\frac{|OQ|}{|OP|}$.

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