
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 line $l$ passing through point $A(1, 1)$ with a slope of $-m$ ($m > 0$) intersects the x-axis and y-axis at points $P$ and $Q$, respectively. Perpendicular lines are drawn from $P$ and $Q$ to the line $2x + y = 0$, and the feet of the perpendiculars are $R$ and $S$,  
(1) Express the lengths of $PR$, $QS$, and $SR$ in terms of $m$.  
(2) Find the minimum area of the quadrilateral $PRSQ$.

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