
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 that points $P$ and $Q$ are two moving points on the circle $O: x^{2}+y^{2}=5$, and point $A$ is a fixed point on the line $l: x+y-4=0$, find the coordinates of the point $A$ such that the maximum value of $\angle PAQ$ is $90^{\circ}$.

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