
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 equation of line $C_{1}$ is $\begin{cases} x = 1 + t \\ y = 7 + t \end{cases} (t \text{ is the parameter})$, and in the polar coordinate system with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis, the equation of curve $C_{2}$ is $\rho = -2 \cos \theta + 2 \sin \theta$. The minimum distance from any point on curve $C_{2}$ to line $C_{1}$ is $\_\_\_\_\_\_\_.$

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