
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 below, determine the length of side $y$.

[asy]
import olympiad;
draw((0,0)--(2,0)--(0,2)--cycle);
draw((0,0)--(-sqrt(2),0)--(0,2)--cycle);
label("10",(-sqrt(2)/2,1),NW);
label("$y$",(1,1),NE);
draw("$30^{\circ}$",(2.1,0),NW);
draw("$45^{\circ}$",(-1.4,0),NE);
draw(rightanglemark((0,2),(0,0),(2,0),4));
[/asy]

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