
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
Given a regular pentagon, let \( M \) be an arbitrary point inside it (or on its boundary). Number the distances from point \( M \) to the sides of the pentagon (or their extensions) in ascending order: \( r_{1} \leqslant r_{2} \leqslant r_{3} \leqslant r_{4} \leqslant r_{5} \). Find all positions of point \( M \) where \( r_{3} \) achieves its minimum value, and all positions of point \( M \) where \( r_{3} \) achieves its maximum value.

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