
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 $A(0,1,0)$, $B(1,1,0)$, $C(1,0,0)$, and point $P(x,y,1)$, if $PA \perp$ plane $ABC$, then the coordinates of point $P$ are ______.

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