
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
In rectangle $LMNO$, points $P$ and $Q$ quadruple $\overline{LN}$, and points $R$ and $S$ quadruple $\overline{MO}$. Point $P$ is at $\frac{1}{4}$ the length of $\overline{LN}$ from $L$, and point $Q$ is at $\frac{1}{4}$ length from $P$. Similarly, $R$ is $\frac{1}{4}$ the length of $\overline{MO}$ from $M$, and $S$ is $\frac{1}{4}$ length from $R$. Given $LM = 4$, and $LO = MO = 3$. Find the area of quadrilateral $PRSQ$.

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