A key problem in Belief-Desire-Intention agents is how an agent progresses its intentions, i.e., which plans should be selected and how the execution of these plans should be interleaved so as to achieve the agent's goals. Previous approaches to the intention progression problem assume the agent has perfect information about the state of the environment. However, in many real-world applications an agent may be uncertain about whether an environment condition holds, and hence whether a particular plan is applicable or an action is executable. In this paper, we propose SAU, a Monte-Carlo Tree Search (MCTS)-based solver for intention progression problems where the agent's beliefs are uncertain. We evaluate the performance of our approach experimentally by varying the degree of uncertainty in the agent's beliefs. The results suggest that SAU is able to successfully achieve the agent's goals even in settings where there is significant uncertainty in the agent's beliefs.