
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 $x$ in the following diagram:

[asy]
import olympiad;

draw((0,0)--(2,0)--(0,2*sqrt(2))--cycle);
draw((0,0)--(-2,0)--(0,2*sqrt(2))--cycle);
label("10",(-1, sqrt(2)),NW);
label("$x$",(sqrt(2),sqrt(2)),NE);
draw("$30^{\circ}$",(2.2,0),NW);
draw("$45^{\circ}$",(-1.8,0),NE);

draw(rightanglemark((0,2*sqrt(2)),(0,0),(2,0),4));
[/asy]

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