
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
\( AB \) and \( CD \) are two non-intersecting chords, with \( \angle A B = 120^{\circ} \) and \( \angle C D = 90^{\circ} \). \( M \) is the intersection point of chords \( AD \) and \( BC \). Find the areas of triangles \( AMB \) and \( CMD \), given that the sum of these areas equals 100.

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