
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
Inside triangle \( ABC \), a random point \( M \) is chosen. What is the probability that the area of one of the triangles \( ABM \), \( BCM \), or \( CAM \) will be greater than the sum of the areas of the other two?

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