
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
Determine the length of $y$ in the following diagram:

[asy]
import olympiad;
draw((0,0)--(2,0)--(0,2)--cycle);
draw((0,0)--(-1,0)--(0,2)--cycle);
label("10",(-1/2,1),NW);
label("$y$",(1,1),NE);
draw("$50^{\circ}$",(1.8,0),NW);
draw("$60^{\circ}$",(-0.9,0),NE);
draw(rightanglemark((0,2), (0,0), (2,0), 4));
[/asy]

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