
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
In rectangle \(ABCD\), \(A B: AD = 1: 2\). Point \(M\) is the midpoint of \(AB\), and point \(K\) lies on \(AD\), dividing it in the ratio \(3:1\) starting from point \(A\). Find the sum of \(\angle CAD\) and \(\angle AKM\).

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