
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 diagram, square $WXYZ$ has sides of length $5,$ and $\triangle WXF$ is equilateral. Line segments $XF$ and $WY$ intersect at $R.$ Point $S$ is on $YZ$ so that $RS$ is perpendicular to $YZ$ and $RS=y.$ [asy]
pair W, X, Y, Z, F, R, S;
W=(0,0);
X=(5,0);
Y=(5,-5);
Z=(0,-5);
F=(2.5,-4.330);
R=(3.18,-3.18);
S=(5,-3.18);
draw(W--X--Y--Z--W--F--X);
draw(W--Y);
draw(R--S, dashed);
label("W", W, NW);
label("X", X, NE);
label("Y", Y, SE);
label("Z", Z, SW);
label("F", F, S);
label("R", R, W);
label("S", S, dir(0));
label("$y$", (R+S)/2, N);
label("5", (W+X)/2, N);
[/asy]
Determine the measure of angle $RYS.$

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