
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 \( \angle ACB \). 

[asy]
import markers;

real t=.5; // Changed for simplicity in calculations
pair A=(0,0);
pair B=(4,3); // Changed coordinates to modify lengths
pair C=(1,2.5); // Adjusted for a new angle bisector setup
pair X=t*A+(1-t)*B;
pair D=(3, 2.25); // New point on AB

draw(C--A--B--C--X);
draw(C--D, dashed); // Added a new line segment

label("$A$",A,SW);
label("$B$",B,E);
label("$C$",C,N);
label("$X$",X,SE);
label("$D$", D, E);

// Modifying lengths for the problem
label("$35$", .5*(B+X), SE);
label("$40$", .5*(B+C), N);
label("$25$", .5*(A+C), NW);
label("$20$", .5*(B+D), E); // New label for BD

[/asy]

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