
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 the trapezoid \( ABCD \), angles \( A \) and \( D \) are right angles, \( AB = 1 \), \( CD = 4 \), \( AD = 5 \). Point \( M \) is taken on side \( AD \) such that \(\angle CMD = 2 \angle BMA \).

In what ratio does point \( M \) divide side \( AD \)?

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