
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
What is the value of $y$ in the diagram?

[asy]
import olympiad;

draw((0,0)--(sqrt(2),sqrt(2))--(0,sqrt(2))--cycle);
draw((0,0)--(-1,0)--(0,sqrt(2))--cycle);

label("6",(-0.5,sqrt(2)/2),W);
label("$y$",(sqrt(2)/4,sqrt(2)/1.5),NE);
draw("$45^{\circ}$",(sqrt(2)/2,sqrt(2)/2),SE);
draw("$60^{\circ}$",(-0.5,0),S);
draw(rightanglemark((0,sqrt(2)),(0,0),(sqrt(2),sqrt(2)),4));
[/asy]

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