
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

On the side $AB$ of triangle $ABC$, a point $M$ is taken. It starts moving parallel to $BC$ until it intersects $AC$, then it moves parallel to $AB$ until it intersects $BC$, and so on. Is it true that after a certain number of such steps, the point $M$ will return to its original position? If true, what is the minimum number of steps required for the return?

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