
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 $u, v, w,$ and $x$ be positive real numbers such that:
\[\begin{array}{c@{\hspace{3pt}}c@{\hspace{3pt}}c@{\hspace{3pt}}c@{\hspace{3pt}}c}
u^2 + v^2 &=& w^2 + x^2 &=& 3005, \\
uw &=& vx &=& 1729.
\end{array}\]
If $T = u+v+w+x$, compute the value of $\lfloor T \rfloor$.

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