
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
Find the length $x$ in the following geometric configuration:

[asy]
unitsize(0.7 cm);

pair A, B, C, D, O;

O = (0,0);
A = 5*dir(160);
B = 6*dir(160 + 180);
C = 9*dir(20);
D = 5*dir(20 + 180);

draw(A--B);
draw(C--D);
draw(A--C);
draw(B--D);

label("$5$", (A + O)/2, SW);
label("$11$", (C + O)/2, SE);
label("$5$", (D + O)/2, NW);
label("$6$", (B + O)/2, NE);
label("$9$", (B + D)/2, S);
label("$x$", (A + C)/2, N);
label("$A$", A, W);
label("$B$", B, E);
label("$C$", C, E);
label("$D$", D, W);
label("$O$", O, N);
[/asy]

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