
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 updated diagram?

[asy]
import olympiad;

draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);
draw((0,0)--(-1,0)--(0,1)--cycle);

label("6",(-1/2,1/2),NW);
label("$y$",(sqrt(3)/2,sqrt(3)/2),NE);

draw("$45^{\circ}$",(1.5,0),NW);
draw("$45^{\circ}$",(-0.9,0),NE);

draw(rightanglemark((0,1),(0,0),(sqrt(3),0),4));
[/asy]

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