
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
The sides of an acute-angled triangle \( ABC \) are \( a, b, \) and \( c \) respectively. Point \( M \) is located inside the triangle. The angles \( \angle AMB, \angle BMC, \) and \( \angle CMA \) are equal to each other. Find the sum of the segments \( AM, BM, \) and \( CM \).

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