
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 quadrilateral \(ABCD\), side \(AB\) is equal to diagonal \(AC\) and is perpendicular to side \(AD\), while diagonal \(AC\) is perpendicular to side \(CD\). On side \(AD\), a point \(K\) is chosen such that \(AC = AK\). The angle bisector of \(\angle ADC\) intersects \(BK\) at point \(M\). Find \(\angle ACM\).

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