
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 $BC$ of rectangle $ABCD$, a point $K$ is marked. There is a point $H$ on the segment $AK$ such that $\angle AHD=90^{\circ}$. It turns out that $AK=BC$. How many degrees is $\angle ADH$ if $\angle CKD=71^\circ$?

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