
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
Let \(ABCD\) be an isosceles trapezoid such that \(AD = BC\), \(AB = 3\), and \(CD = 8\). Let \(E\) be a point in the plane such that \(BC = EC\) and \(AE \perp EC\). Compute \(AE\).

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