
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
Let point $P$ be a moving point on the parabola $x^2=4y$, and the distance from point $P$ to the $x$-axis is $d$. Point $P_1$ is a moving point on the circle $(x-2)^2+(y+1)^2=1$. When $d+|PP_1|$ is minimized, the coordinates of point $P$ are ______.

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