Question: Solving a system of 6 equations for 6 unknowns

I am trying to find 6 unknowns A, B, C, L, E, and F and have managed to write down a system of 6 equations involving these unknowns.  However, the equations are long and which I try to put the system together and solve with solve(sys, {A, B, C, E, F, L}) it says `[Length of output exceeds limit of 1000000]`.  Although the equations are long, I feel like something must be going wrong as the output cannot be that long.  The equations are:

C = (((h/(4*Pi*K)*H*e^(-k*h)*I/k - k*h^2/2 + H*A*e^(-k*h)*I/(K*k^2) - B*h - sqrt(Pi/2)*h/(2*Pi)*H*e^(-k*h)*I + sqrt(Pi/2)*K*k*h - sqrt(Pi/2)*H*A*e^(-k*h)*I/k + sqrt(Pi/2)*B*K - sqrt(Pi/2)*K*H*k*h^2*I/2) + sqrt(Pi/2)*H*A*e^(-k*h)*I/k) - sqrt(Pi/2)*H*F*h*K*I - sqrt(Pi/2)*H*A*e^(-k*h)*I/k + sqrt(Pi/2)*K*H*k*h^2/2*I) - sqrt(Pi/2)*H*F*h*K*I,

E = (((h/(4*Pi*K)*J*e^(-k*h)*I/k - k*h^2/2 + J*A*e^(-k*h)*I/(K*k^2) - L*h - sqrt(Pi/2)*h/(2*Pi)*J*e^(-k*h)*I + sqrt(Pi/2)*K*k*h - sqrt(Pi/2)*J*A*e^(-k*h)*I/k + sqrt(Pi/2)*L*K - sqrt(Pi/2)*K*J*k*h^2*I/2) + sqrt(Pi/2)*J*A*e^(-k*h)*I/k) - sqrt(Pi/2)*J*F*h*K*I - sqrt(Pi/2)*J*A*e^(-k*h)*I/k + sqrt(Pi/2)*K*J*k*h^2/2*I) - sqrt(Pi/2)*J*F*h*K*I

0 = -H*(k*z^2/2 - H*A*e^(-k*z)*I/(K*k^2) + B*z + C)*I - J*(k*z^2/2 - J*A*e^(-k*z)*I/(K*k^2) + L*z + E)*I + k*z + A*e^(-k*z)/K + F

0 = ((-H*A*e^(-k*z)*I - H*I*(-2*K*(-H*k*z^2*I/2 - H^2*A*e^(-k*z)/(K*k^2) - H*B*z*I - H*C*I)) - J*I*(-2*K*1/2*(((-J*k*z^2*I/2 - J*H*A*e^(-k*z)/(K*k^2) - J*B*z*I - J*C*I - H*k*z^2*I/2) - J*H*A*e^(-k*z)/(K*k^2)) - H*L*z*I - i*H*E)) - K*k) + H*A*e^(-k*z)*I) + K*H*z*k*I + H*A*e^(-k*z)*I + K*H*F*I

0 = ((-J*A*e^(-k*z)*I - H*(((K*J*k*z^2*I/2 + J*H*A*e^(-k*z)/k^2 + K*J*B*z*I + k*h*K*z^2*I/2) + J*H*A*e^(-k*z)/k^2) + K*H*L*z*I + K*H*E*I)*I - J*I*(-2*K*(-J*k*z^2*I/2 - J^2*A*e^(-k*z)/(K*k^2) - J*L*z*I - J*E*I)) - K*k) + J*A*e^(-k*z)*I) + K*J*z*k*I + J*A*e^(-k*z)*I + K*J*F*I

0 = (-k*A*e^(-k*z) - H*I*(-2*K*1/2*(((k*z + H*A*e^(-k*z)*I/(K*k) + B - H*k*z^2*I/2) + H*A*e^(-k*z)*I/(K*k)) - H*F*z*I - H*G*I)) - J*I*(-2*K*1/2*(((k*z + J*A*e^(-k*z)*I/(K*k) + L - J*k*z^2*I/2) + J*A*e^(-k*z)*I/(K*k)) - J*F*z*I - J*G*I)) - 2*K*k) + 2*k*A*e^(-k*z)

where h takes a constant value, H and J are constants, k is the square root of H^2 + J^2, I is the imaginary unit, and z also takes some value as a parameter.