
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 circle C: $(x^2+y^2-4x-4y+4=0)$, and point $E(3,4)$.
(1) The line $l$ passing through point $E$ intersects the circle at points $A$ and $B$. If $AB=2 \sqrt {3}$, find the equation of line $l$.
(2) From a point $P(x_{1},y_{1})$ outside the circle C, a tangent line is drawn to the circle, with the point of tangency denoted as $M$. $O$ represents the origin of the coordinate system, and $PM=PO$. Find the coordinates of point $P$ when $PM$ is at its minimum value.

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