I am confused on how to do this problem, explanation of steps to solve would be much appreciated.

Problem 3. Consider an American put option when the stock price is $32, the exercise price is $30, the time to maturity is six months, the volatility is 20% per annum, and the risk-free interest rate is 5% per annum. Two dividends are expected during the life of the option with ex-dividend dates at the end of two months and five months. Each of the dividends is 50 cents. (a) Divide the option's time to maturity into six time steps to generate a tree for the "pure" stock price that excludes the value of the expected dividends and display the tree in a table like the one provided at the end of this problem. Present all values with three decimal digits. (b) Calculate the value of the expected dividends at each time step to generate a six-step tree for the market" stock price that includes the value of the expected dividends. Display the dividend values and the tree in the table. (c) Use the "market" price tree to calculate the value of the put option and display the option values in the table. (d) Does early exercise happen? If yes, in which steps does it happen? Does it happen right before ex-dividend date? Problem 3. Consider an American put option when the stock price is $32, the exercise price is $30, the time to maturity is six months, the volatility is 20% per annum, and the risk-free interest rate is 5% per annum. Two dividends are expected during the life of the option with ex-dividend dates at the end of two months and five months. Each of the dividends is 50 cents. (a) Divide the option's time to maturity into six time steps to generate a tree for the "pure" stock price that excludes the value of the expected dividends and display the tree in a table like the one provided at the end of this problem. Present all values with three decimal digits. (b) Calculate the value of the expected dividends at each time step to generate a six-step tree for the market" stock price that includes the value of the expected dividends. Display the dividend values and the tree in the table. (c) Use the "market" price tree to calculate the value of the put option and display the option values in the table. (d) Does early exercise happen? If yes, in which steps does it happen? Does it happen right before ex-dividend date