
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
In the diagram below, $AB = 60$ cm. Point $C$ is on line segment $AB$ but not at the midpoint. The length of $BC$ is 40 cm and $AC$ is 20 cm. Point $X$ lies on segment $AB$ such that $\angle CXA = \angle CXB$. Find the length of $AX$.

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