Assume abrupt clipping of the amplifier, not gradual

An amplifier has output voltage limits of L- = -6 V and L+ = +4 V and has an open circuit voltage gain of Avo = -5. A sinusoidal input centered at 0 V (so no bias voltage) having a peak voltage of X volts is applied to the amplifier.

a) What is the largest peak voltage (amplitude) of the output for no clipping to occur?

b ) What then is the largest value of input voltage X to have no clipping?

c) Can the output voltage be biased such that a larger peak output voltage is obtained? If so, what is the bias and what are the new peak output and input voltages?

My intuition was that maximum output would be +4 V and max input would then be -4/5 V (by Vi = Vo/Avo), but I wasn't sure. Would greatly appreciate a detailed explanation. Thanks.

Small diagram I drew:

a) A max output of 4V peak can be obtained as the input is centered at 0V.
A max input that can be applied is X x (5) = 4. So largest input is 800mV. Remember the negative sign represents a 180 degree phase shift.
c) The input could be biased by -1V. The new peak output voltage would become 5V. The peak input voltage would become 1 volt.

Does that all make sense? Fg?