
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
 $ABCD$  is an isosceles trapezium such that  $AD=BC$ ,  $AB=5$  and  $CD=10$ . A point  $E$  on the plane is such that  $AE\perp{EC}$  and  $BC=EC$ . The length of  $AE$  can be expressed as  $a\sqrt{b}$ , where  $a$  and  $b$  are integers and  $b$  is not divisible by any square number other than  $1$ . Find the value of  $(a+b)$ .

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