
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 Cartesian coordinate system $(xOy)$, a curve $C_{1}$ is defined by the parametric equations $x=\cos{\theta}$ and $y=\sin{\theta}$, and a line $l$ is defined by the polar equation $\rho(2\cos{\theta} - \sin{\theta}) = 6$.

1. Find the Cartesian equations for the curve $C_{1}$ and the line $l$.
2. Find a point $P$ on the curve $C_{1}$ such that the distance from $P$ to the line $l$ is minimized, and compute this minimum distance.

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