
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
Let $O$ be the center of a circle with radius 1. Let points $A$, $B$, $C$, and $D$ lie on the circle such that $AB$ is a diameter and $CD$ is a chord. Point $X$ is on the circle such that $OX$ bisects $\angle CXD$. If $\angle AXB = 90^\circ$ and $3\angle BAC = \angle CXD = 72^\circ$, calculate the length $AX$.

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