
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
Let $p, q, r$, and $s$ be positive real numbers such that
\[\begin{array}{c@{\hspace{3pt}}c@{\hspace{3pt}}c@{\hspace{3pt}}c@{\hspace{3pt}}c}p^2+q^2&=&r^2+s^2&=&3024,\\ pr&=&qs&=&1500.\end{array}\]
Compute the value of $\lfloor T \rfloor$, where $T=p+q+r+s$.

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