
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
A circumcircle is drawn around an isosceles triangle \(ABC\) where \(AB=AC\). A tangent to the circle at point \(B\) intersects the ray \(AC\) at point \(D\). Let \(E\) be the midpoint of side \(AB\), and \(H\) be the foot of the perpendicular dropped from point \(D\) to line \(AB\). Find the length \(EH\) if \(AD=a\).

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