
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
Find \(AX\) in the diagram if \(CX\) bisects \(\angle ACB\) in triangle \(ABC\), where \(AB = 45\) units, \(BC = 55\) units, \(AC = 33\) units, and \( \angle ACB = 60^\circ \).

[asy]
import markers;

real t=.56;
pair A=(0,0);
pair B=(5,0);
pair C=(2,1.5);
pair X=t*A+(1-t)*B;

draw(C--A--B--C--X);
label("$A$",A,SW);
label("$B$",B,E);
label("$C$",C,N);
label("$X$",X,S);

label("$33$", (.5*(A + C)), W);
label("$55$", (.5*(B + C)), E);
label("$45$", (.5*(A + B)), S);
[/asy]

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