
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 line $C_1$: 
$$
\begin{cases} 
x=1+ \frac { \sqrt {2}}{2}t \\ 
y= \frac { \sqrt {2}}{2}t
\end{cases}
$$
(where $t$ is a parameter), and the curve $C_2$: 
$$
\begin{cases} 
x=r\cos\theta \\ 
y=r\sin\theta
\end{cases}
$$
(where $r>0$, $\theta$ is a parameter).

(1) When $r=1$, find the coordinates of the intersection points between $C_1$ and $C_2$;

(2) Let point $P$ be a moving point on curve $C_2$, when $r= \sqrt {2}$, find the coordinates of point $P$ when the distance from $P$ to line $C_1$ is maximized.

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