
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 side $y$ in the following diagram:

[asy]
import olympiad;

draw((0,0)--(4,0)--(2,2*sqrt(3))--cycle);
draw((0,0)--(-sqrt(3),0)--(2,2*sqrt(3))--cycle);

label("10",(-sqrt(3)/2,2*sqrt(3)/3),NW);
label("$y$",(3,2*sqrt(3)/3),NE);

draw("$30^\circ$",(4.2,0),NW);
draw("$45^\circ$",(-sqrt(3)-0.6,0),NE);

draw(rightanglemark((2,2*sqrt(3)),(0,0),(4,0),4));

[/asy]

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