
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
On the side \(AB\) of an equilateral triangle \(\mathrm{ABC}\), a right triangle \(\mathrm{A H B}\) is constructed (\(\mathrm{H}\) is the vertex of the right angle) such that \(\angle \mathrm{HBA}=60^{\circ}\). Let point \(K\) lie on the ray \(\mathrm{BC}\) beyond point \(\mathrm{C}\) such that \(\angle \mathrm{CAK}=15^{\circ}\). Find the angle between the line \(\mathrm{HK}\) and the median of triangle \(\mathrm{AHB}\) extended from vertex \(\mathrm{H}\).

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