
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 circle with center A($m$, $\frac{2}{m}$) ($m \in \mathbb{R}$ and $m > 0$) intersects the x-axis at points O and B, and intersects the y-axis at points O and C, where O is the origin.  
(1) When $m=2$, find the standard equation of circle A;  
(2) When $m$ varies, is the area of $\triangle OBC$ a constant? If yes, find the constant value; if no, explain why;  
(3) Suppose the line $l: 2x+y-4=0$ intersects circle A at points P and Q, and $|OP|=|OQ|$, find the value of $|PQ|$.

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