Question: How do I Solve in Maple with conditions in Domain and Range with only Real solutions

How do I find the solutions "links" with only answers in the range 0 to +1? The domain of vgl is 0 <=beta <= 1. If the system is inconsistent or insufficient to solve xi (for example, if xi does not appear in the equation) then give the text "no solution". If there is a solution then show it. Filter only real solutions. Please help me with better code:

restart;
assume(beta > 0, beta < 1):
interface(showassumed=0):

vgl[1] := -((beta*xi^2 + 2*xi^2 - beta)*(beta - 1)^2)/4 = 0:  # or some other equation (sometimes xi does not appear in the equation)

if has(lhs(vgl[1]), xi) or has(rhs(vgl[1]), xi) then
    links := solve([vgl[1], xi > 0, xi < beta], xi):
    # Filter only real solutions
    links_real := select(x -> type(x, equation) and is(Im(rhs(x)) = 0), [links]):
    if nops(links_real) > 0 then
        x1 := links_real;
        print("Real solution(s):", x1);
    else
        print("No real solution in range for xi.");
    end if;
else
    print("The equation does not contain xi — solving for xi is not possible.");
end if;