
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
In the right triangle  $ABC$  shown,  $E$  and  $D$  are the trisection points of the hypotenuse  $AB$ . If  $CD=7$  and  $CE=6$ , what is the length of the hypotenuse  $AB$ ? Express your answer in simplest radical form.

[asy]
pair A, B, C, D, E;
A=(0,2.9);
B=(2.1,0);
C=origin;
D=2/3*A+1/3*B;
E=1/3*A+2/3*B;
draw(A--B--C--cycle);
draw(C--D);
draw(C--E);
label(" $A$ ",A,N);
label(" $B$ ",B,SE);
label(" $C$ ",C,SW);
label(" $D$ ",D,NE);
label(" $E$ ",E,NE);
[/asy]

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