IMAS 2025-2026 Junior Division - First Round Question 5

As shown in the diagram below, $ABC$ is a triangle where $\angle ABC>\angle BAC=60^\circ$, $AB=1$ cm and $AC=2\sqrt3$ cm. If the perpendicular bisector of $AC$ intersects line $AB$ at point $M$, what is the length, in cm, of $MB$?