
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 trapezoid $ABCD$, angles $A$ and $D$ are right angles, $AB=1$, $CD=4$, $AD=5$. A 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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