
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 a right triangle \(ABC\), a circle is constructed on the leg \(AC\) as its diameter, intersecting the hypotenuse \(AB\) at point \(E\). A tangent to the circle is drawn through point \(E\), which intersects the leg \(CB\) at point \(D\). Find the length \(DB\) if \(AE = 6\) and \(BE = 2\).

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