
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
 $\triangle ABC$  has area  $240$ . Points  $X, Y, Z$  lie on sides  $AB$ ,  $BC$ , and  $CA$ , respectively. Given that  $\frac{AX}{BX} = 3$ ,  $\frac{BY}{CY} = 4$ , and  $\frac{CZ}{AZ} = 5$ , find the area of  $\triangle XYZ$ .

[asy]
size(175);
defaultpen(linewidth(0.8));
pair A=(0,15),B=(0,-5),C=(25,0.5),X=origin,Y=(4C+B)/5,Z=(5A+C)/6;
draw(A--B--C--cycle^^X--Y--Z--cycle);
label(" $A$ ",A,N);
label(" $B$ ",B,S);
label(" $C$ ",C,E);
label(" $X$ ",X,W);
label(" $Y$ ",Y,S);
label(" $Z$ ",Z,NE);[/asy]

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