
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 triangle $ABC$, points $A$, $B$, and $C$ are located such that $AB = 35$ units, $BC = 40$ units, and $CA = 45$ units. A point $X$ lies on side $AB$ such that $CX$ bisects $\angle ACB$. Given that $BX = 21$ units, find the length of segment $AX$.

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