
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 $\triangle ABC$ be a triangle with $A$, $B$, and $C$ as vertices, and point $X$ lies on line segment $AB$. $X$ is such that line segment $CX$ bisects $\angle ACB$. Given that $AC = 36$, $BC = 40$, and $BX = 25$, find the length of $AX$.

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