
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 diagram, if $\angle ABC = 60^\circ$, what is the measure of $\angle AMD$? [asy]

size(6cm);

pair a = (0, 0); pair m = dir(180 - 30); pair d = dir(180 + 30); pair c = 1.3 * dir(30); pair b = 2 * 1.3 * Cos(60) * dir(-30);

label("$M$", m, N); label("$C$", c, N); label("$A$", a, 1.5 * S); label("$D$", d, S); label("$B$", b, SE);

draw(m--b--c--d--cycle);

add(pathticks(m--a, s=4));

add(pathticks(d--a, s=4));

add(pathticks(c--a, 2, spacing=0.9, s=4));

add(pathticks(c--b, 2, spacing=0.9, s=4));

[/asy]

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