I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $600$ pounds more than each of her trucks, but no more than $\frac{1}{3}$ of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?
Your truck: $T$
Neighbor: $t$
$T\ge t+600$
$T\le \frac{4t}{3}$
Solve the inequality chain.