
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 \(A B C D E F\) be a convex equilateral hexagon such that lines \(B C\), \(A D\), and \(E F\) are parallel. Let \(H\) be the orthocenter of triangle \(A B D\). If the smallest interior angle of the hexagon is 4 degrees, determine the smallest angle of the triangle \(H A D\) in degrees.

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