
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 $l$ passing through the point $P(-1,0)$: $ \begin{cases} x= \frac { \sqrt {2}}{2}t-1 \\ y= \frac { \sqrt {2}}{2}t\\ \end{cases}$ (where $t$ is a parameter) intersects the circle $x^{2}+y^{2}-2x-4y+4=0$ at points $M$ and $N$. Find the coordinates of the midpoint of $MN$.

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