
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 shown diagram, segment $CD$ is parallel to segment $WX$. If $CX = 30$ units, $DP = 15$ units, and $PW = 45$ units, find the length of segment $PX$. Diagram:
[asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
pair W = (0,0), X = (24,0), C = (0,12), D = (9,12);
draw(C--D--W--X--cycle);
label("$C$",C,W); label("$D$",D,E); label("$W$",W,W); label("$X$",X,E);
pair P = intersectionpoint(C--X,D--W);
label("$P$",P,E);
[/asy]

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