
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
A right triangle $XYZ$ is such that angle $YXZ$ is $45^\circ$ and the length $YZ$ is $10$. Calculate the length of $XZ$. 

[asy]
unitsize(1inch);
pair X,Z,Y;
X = (0,0);
Z = (1,0);
Y = (0,1);
draw(X--Z--Y--X);
draw(rightanglemark(Z, X, Y, 3));
label("$X$",X,S);
label("$Z$",Z,S);
label("$Y$",Y,N);
label("$10$",Y/2,W);
label("$45^\circ$", (0.5, 0), N);
[/asy]

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