
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Points $A$, $B$, $C$, and $D$ lie on a circle of radius 1 unit. Point $X$ lies on the circle such that $\overline{AX}$ is a diameter. If $\angle BXC = 24^\circ$ and $\angle BAC = \angle CAD = 24^\circ$, determine the length $BX$.

Present the answer in LaTex format: \boxed{Your answer}
user