
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, with the origin $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. For line $L: \rho\cos\theta - \sqrt{3}\rho\sin\theta + 1 = 0$, and the parametric equation of curve $C$ is $\begin{cases} x=5+\cos\alpha \\ y=\sin\alpha\end{cases}$ (where $\alpha$ is the parameter).

(Ⅰ) Find the standard equations of line $L$ and curve $C$;  
(Ⅱ) Find a point $Q$ on curve $C$ such that the distance from $Q$ to line $L$ is minimized, and find this minimum value.

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