
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

Given a right isosceles triangle $ABC$ with hypotenuse $AB$. Point $M$ is the midpoint of side $BC$. Point $K$ is chosen on the smaller arc $AC$ of the circumcircle of triangle $ABC$. Point $H$ is the foot of the perpendicular dropped from $K$ to line $AB$. Find the angle $\angle CAK$, given that $KH = BM$ and lines $MH$ and $CK$ are parallel.

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