Sequential Multiple Assignment Randomized Trials (SMART) provide a framework for testing dynamic treatment strategies, which are pre-specified rules for re-randomizing participants based on their responses. We extend the fixed SMART design to include an Internal Pilot Study for feasibility and unblinded Sample Size Re-estimation (SSR). We apply the one-stage exact test for feasibility, and Adjusted Effect Size (AES) and Cui, Hung, Wang (CHW) methods for SSR. We assess the statistical properties of our design in terms of expected re-estimated sample size, type I error rate and statistical power using simulations. Results show that both SSR methods perform well in controlling type I error inflation and keeping the power over 80% after appropriate adjustment. Both methods recover the power compared to the fixed design when the true effect size is smaller than planned, while the CHW method performs slightly better in terms of power and requires a smaller sample size than the AES method.