
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 a polar coordinate system with the pole at the origin \( O \) of the Cartesian coordinate system, where the polar axis coincides with the non-negative half of the \( x \)-axis, and the length unit is the same, the polar equation of line \( l \) is \( \rho\sin (\theta - \frac{\pi}{6})=5 \). The curve \( C \) is described by the parametric equations \( \begin{cases} x=\sqrt{2}\cos \alpha \\ y=-2+\sqrt{2}\sin \alpha \end{cases} \), where \( \alpha \in [0,2\pi) \).
(1) Write out the Cartesian equation of the line \( l \) and the ordinary equation of the curve \( C \).
(2) If point \( P \) is a moving point on the curve \( C \), find the maximum distance from point \( P \) to the line \( l \).

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