
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
The parametric equations of curve $C_1$ are: 
$$
\begin{cases} 
x=1+t\cos \frac {\pi}{4} \\
y=5+t\sin \frac {\pi}{4}
\end{cases}
$$
($t$ is the parameter), and the parametric equations of curve $C_2$ are: 
$$
\begin{cases} 
x=\cos\phi \\
y= \sqrt {3}\sin\phi
\end{cases}
$$
($\phi$ is the parameter).

(1) Find the general equation of curve $C_2$. If the coordinate origin is taken as the pole and the positive half-axis of $x$ as the polar axis to establish the coordinate system, find the polar coordinate equation of curve $C_1$.

(2) If point $P$ is any point on curve $C_2$, find the minimum distance from point $P$ to curve $C_1$.

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