
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
Given the Cartesian coordinate system \(xOy\), the equation of the curve \(C\) is 
$$
\begin{cases} 
x = 2\cos φ \\ 
y = -\sqrt{3} + 2\sin φ
\end{cases}
(φ \text{ is the parameter}).
$$
A polar coordinate system is established with \(O\) as the pole and the non-negative half-axis of \(x\) as the polar axis. The polar coordinates of point \(P\) are \((2\sqrt{3}, \frac{π}{6})\), and the polar coordinate equation of line \(l\) is \(4ρ\cos θ + 3ρ\sin θ + 1 = 0\).

(1) Write down the Cartesian coordinates of point \(P\) and the ordinary equation of curve \(C\);
(2) If \(Q\) is a moving point on curve \(C\), find the minimum distance from the midpoint \(M\) of \(PQ\) to line \(l\).

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